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COURSE MANUAL
Operations Management in Educational Practices
EME 302
University of Ibadan Distance Learning Centre
Open and Distance Learning Course Series Development
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Copyright © 2015 by Distance Learning Centre, University of Ibadan, Ibadan.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
System, or transmitted in any form or by any means, electronic, mechanical,
photocopying, recording or otherwise, without the prior permission of the copyright
owner.
ISBN 978-021-899-8
General Editor: Prof. Bayo Okunade
University of Ibadan Distance Learning Centre
University of Ibadan, Nigeria
Telex: 31128NG
Tel: +234 (80775935727) E-mail: [email protected]
Website: www.dlc.ui.edu.ng
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Vice-Chancellor’s Message The Distance Learning Centre is building on a solid tradition of over two decades of
service in the provision of External Studies Programme and now Distance Learning
Education in Nigeria and beyond. The Distance Learning mode to which we are
committed is providing access to many deserving Nigerians in having access to higher
education especially those who by the nature of their engagement do not have the luxury
of full time education. Recently, it is contributing in no small measure to providing places
for teeming Nigerian youths who for one reason or the other could not get admission into
the conventional universities.
These course materials have been written by writers specially trained in ODL course
delivery. The writers have made great efforts to provide up to date information,
knowledge and skills in the different disciplines and ensure that the materials are user-
friendly.
In addition to provision of course materials in print and e-format, a lot of Information
Technology input has also gone into the deployment of course materials. Most of them
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you listen to the audio study sessions. Some of the study session materials have been
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others have been delivered and captured in audio-visual format in a classroom
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available on the website. We will continue in our efforts to provide and review course
materials for our courses.
However, for you to take advantage of these formats, you will need to improve on your
I.T. skills and develop requisite distance learning Culture. It is well known that, for
efficient and effective provision of Distance learning education, availability of
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multiple plat form for the convenience of our students. It is in fulfilment of this, that
series of course materials are being written to enable our students study at their own pace
and convenience.
It is our hope that you will put these course materials to the best use.
Prof. Abel Idowu Olayinka
Vice-Chancellor
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Foreword As part of its vision of providing education for “Liberty and Development” for Nigerians
and the International Community, the University of Ibadan, Distance Learning Centre has
recently embarked on a vigorous repositioning agenda which aimed at embracing a
holistic and all encompassing approach to the delivery of its Open Distance Learning
(ODL) programmes. Thus we are committed to global best practices in distance learning
provision. Apart from providing an efficient administrative and academic support for our
students, we are committed to providing educational resource materials for the use of our
students. We are convinced that, without an up-to-date, learner-friendly and distance
learning compliant course materials, there cannot be any basis to lay claim to being a
provider of distance learning education. Indeed, availability of appropriate course
materials in multiple formats is the hub of any distance learning provision worldwide.
In view of the above, we are vigorously pursuing as a matter of priority, the provision of
credible, learner-friendly and interactive course materials for all our courses. We
commissioned the authoring of, and review of course materials to teams of experts and
their outputs were subjected to rigorous peer review to ensure standard. The approach not
only emphasizes cognitive knowledge, but also skills and humane values which are at the
core of education, even in an ICT age.
The development of the materials which is on-going also had input from experienced
editors and illustrators who have ensured that they are accurate, current and learner-
friendly. They are specially written with distance learners in mind. This is very important
because, distance learning involves non-residential students who can often feel isolated
from the community of learners.
It is important to note that, for a distance learner to excel there is the need to source and
read relevant materials apart from this course material. Therefore, adequate
supplementary reading materials as well as other information sources are suggested in the
course materials.
Apart from the responsibility for you to read this course material with others, you are also
advised to seek assistance from your course facilitators especially academic advisors
during your study even before the interactive session which is by design for revision.
Your academic advisors will assist you using convenient technology including Google
Hang Out, You Tube, Talk Fusion, etc. but you have to take advantage of these. It is also
going to be of immense advantage if you complete assignments as at when due so as to
have necessary feedbacks as a guide.
The implication of the above is that, a distance learner has a responsibility to develop
requisite distance learning culture which includes diligent and disciplined self-study,
seeking available administrative and academic support and acquisition of basic
information technology skills. This is why you are encouraged to develop your computer
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skills by availing yourself the opportunity of training that the Centre’s provide and put
these into use.
In conclusion, it is envisaged that the course materials would also be useful for the
regular students of tertiary institutions in Nigeria who are faced with a dearth of high
quality textbooks. We are therefore, delighted to present these titles to both our distance
learning students and the university’s regular students. We are confident that the
materials will be an invaluable resource to all.
We would like to thank all our authors, reviewers and production staff for the high
quality of work.
Best wishes.
Professor Bayo Okunade
Director
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Course Development Team Content Authoring Prof. Emunemu B.O. & Isuku, E.J
Content Editor
Production Editor
Learning Design/Assessment Authoring
Managing Editor
General Editor
Prof. Remi Raji-Oyelade
Ogundele Olumuyiwa Caleb
Tolulope Famaye
Ogunmefun Oladele Abiodun
Prof. Bayo Okunade
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Table of Contents
Course Overview .................................................................................................................................... xii
Course Objectives ................................................................................................................................... xii
Study Session One The Development of Modern Management Principles ................................. 1
Introduction ............................................................................................................................................... 1
Learning Outcomes for Study Session 1 ................................................................................................... 1
1.1. The Origin and Evolution of Management ................................................................................... 2
1.1.1. Origin of Management .......................................................................................................... 2
1.1.2. The Evolution of Management ............................................................................................. 3
1.2. Modern Management Era.............................................................................................................. 7
1.2.1. Empirical School ................................................................................................................... 7
1.2.2. SocialSchool System ............................................................................................................. 7
1.2.3. Decision Theory School ........................................................................................................ 9
Summary of Session 1 ............................................................................................................................ 10
Self-Assessment Questions (SAQs) for Session 1 .................................................................................. 10
References ............................................................................................................................................... 11
Study Session Two: Programme Evaluation and Review Technique (PERT) .......................... 12
Introduction ............................................................................................................................................. 12
Learning Outcomes for Study Session 2 ................................................................................................. 12
2.1. Meaning and Analysis of Program Evaluation and Review Technique (PERT) ............................. 12
2.1.1. Meaning of Program Evaluation and Review Technique ......................................................... 12
2.1.2. Pert Analysis ............................................................................................................................. 15
2.2. Critical Path Analysis, and Critical Path Method ....................................................................... 16
Summary of Session 2 ............................................................................................................................ 17
Self-Assessment Questions (SAQs) for Session 2 .................................................................................. 17
References ............................................................................................................................................... 18
Study Session Three: Critical Path Method (CPM) ...................................................................... 19
Introduction ............................................................................................................................................. 19
Learning Outcomes for StudySession 3 .................................................................................................. 19
3.1. Meaning, Steps, and Merits, and Demerits of Critical Path Method (CPM) ................................... 19
3.1.1. Meaning of Critical Path Method .............................................................................................. 20
3.1.2. Key Steps in Critical Path Method ............................................................................................ 22
3.1.3 Merits of Critical Path Method .................................................................................................. 24
3.1.4 Demerits of Critical Path Method .............................................................................................. 24
3.2. Critical Chain Project Management (CCPM) .................................................................................. 25
Summary of Session 3 ............................................................................................................................ 26
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Self-Assessment Questions (SAQs) for Session 3 .................................................................................. 27
References ............................................................................................................................................... 27
Study Session Four: Inventory Policy........................................................................................... 29
Introduction ............................................................................................................................................. 29
Learning Outcomes for Study Session 4 ................................................................................................. 29
4.1. Meaning, Methods, and Types of Inventory Policies ...................................................................... 29
4.1.1. Meaning of Inventory Policy .................................................................................................... 29
4.1.2. Inventory Methods best for Organisation ................................................................................. 31
4.1.3. Types of Inventory Policies ...................................................................................................... 31
4.2. Meaning of Stock and Types ........................................................................................................... 34
4.2.1. Stock Reduction ........................................................................................................................ 34
4.2.2. Why the need for Stock? ........................................................................................................... 34
4.3. Economic Order Quantity (EOQ) model ......................................................................................... 36
Summary of Session 4 ............................................................................................................................ 40
Self-Assessment Questions (SAQs) for Session 4 .................................................................................. 41
References ............................................................................................................................................... 42
Study Session Five: Equipment Replacement Policies ................................................................. 43
(Individual and Mass/Group Techniques for Non-Durable Items, Npv and Least Cost Methods
for Durable Items) ......................................................................................................................... 43
Introduction ............................................................................................................................................. 43
Learning Outcomes for Study Session 5 ................................................................................................. 43
5.1. Replacement Theory, Maintenance, and Models in Operation Research ........................................ 44
5.1.1. Replacement Theory inOperation Research .............................................................................. 44
5.1.2. Replacement and Maintenance ................................................................................................. 46
5.1.3. Reasons for Equipment Replacement ....................................................................................... 47
5.1.4. Models in Replacement and Maintenance .......................................................................... 49
5.2. Net Present Value (Npv) and Least Cost Methods .......................................................................... 50
5.2.1. Net Present Value...................................................................................................................... 50
5.2.2. Advantages of Net Present Value (NPV) .................................................................................. 51
5.2.3. Disadvantages of NPV .............................................................................................................. 51
5.2.4.Least Cost Method ..................................................................................................................... 52
Summary of Session 5 ............................................................................................................................ 53
Self-Assessment Questions (SAQs) for Session 5 .................................................................................. 54
References ............................................................................................................................................... 55
Study Session Six: Queuing Theory ............................................................................................. 56
Introduction ............................................................................................................................................. 56
Learning Outcomes for StudySession 6 .................................................................................................. 56
6.1. Meaning and Definition of Terms in Queuing Theory .................................................................... 56
6.1.1. Meaning of Queuing Theory ..................................................................................................... 56
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6.1.2. Definition of Terms inQueuing Model ..................................................................................... 57
Summary of Session 6 ............................................................................................................................ 64
Self-Assessment Questions (SAQs) for Session 6 .................................................................................. 64
References ............................................................................................................................................... 65
Study Session Seven: Total Quality Management in Education .................................................. 66
Introduction ............................................................................................................................................. 66
Learning Outcomes for Study Session 7 ................................................................................................. 66
7.1. Origin, Meaning, and Principles of Total Quality Management ...................................................... 66
7.1.1. The Origin of Total Quality Management ................................................................................ 67
7.1.2. Meaning of Total Quality Management (TQM) ....................................................................... 68
7.1.3. Total Quality Management (TQM)Principles ........................................................................... 71
7.2. The Elements, Generic Model, and Building Blocks of Total Quality Management (TQM) .......... 72
7.2.1. The Primary Elements of TQM ................................................................................................ 72
7.2.2. Generic Model for Implementing TQM .............................................................................. 74
7.2.3. The Buildingblocks of TQM ..................................................................................................... 75
Summary of Session 7 ............................................................................................................................ 77
Self-Assessment Questions (SAQs) for Session 7 .................................................................................. 78
References ............................................................................................................................................... 79
Study Session Eight: Resource Allocation/Assignment: Hungarian Method ............................... 80
Introduction ............................................................................................................................................. 80
Learning Outcomes for Study Session 8 ................................................................................................. 80
8.1. Meaning and Hungarian Method of Resource Allocation ............................................................... 81
8.1.1. Meaning of Resource Allocation .............................................................................................. 81
8.1.2. Hungarian Method for Solving Assignment Problem ............................................................... 81
Summary of Session 8 ............................................................................................................................ 87
Self-Assessment Questions (SAQs) for Session 8 .................................................................................. 88
References ............................................................................................................................................... 89
Study Session Nine: Resource Allocation/Assignment: ........................................................... 90
Transportation Problem I (Simplex and Transportation Method) ................................................ 90
Introduction ............................................................................................................................................. 90
Learning Outcomes for Study Session 9 ................................................................................................. 90
9.1. Meaning of Transportation Problem ................................................................................................ 91
9.2. Variants of the Simplex Method ...................................................................................................... 95
9.2.1. Simplex Method ........................................................................................................................ 95
9.2.2. Transportation Method .............................................................................................................. 97
9.2.3. Methods for Obtaining Basic Feasible Solution for Transportation Problem ........................... 97
Summary of Session 9 ............................................................................................................................ 97
Self-Assessment Questions (SAQs) for Session 9 .................................................................................. 98
References ............................................................................................................................................... 98
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Study Session Ten: Resource Allocation/Assignment: Transportation Problem II (North-West
Rule Model) .................................................................................................................................. 99
Introduction ............................................................................................................................................. 99
Learning Outcomes for Study Session 10 ............................................................................................... 99
10.1. Overview and Meaning of the North-West Rule Model (NWRM) ............................................... 99
10.1.1. Overview of the North-West Rule Model .............................................................................. 99
10.1.2. North-West Corner Method (NWCM) .................................................................................... 99
Summary of Session 10 ........................................................................................................................ 103
Self-Assessment Questions (SAQs) for Session 10 .............................................................................. 104
References ............................................................................................................................................. 104
Study Session Eleven: Resource Allocation/Assignment: Least-Cost Method ....................... 106
Introduction ........................................................................................................................................... 106
Learning Outcomes for Study Session 11 ............................................................................................. 106
11.1. Least Cost Method in Resource Allocation ................................................................................. 106
11.1.1. Minimum Cell-Cost Method ................................................................................................. 107
11.1.2. MODI Method (for obtaining reduced costs) ........................................................................ 108
Summary of Session 11 ........................................................................................................................ 113
Self-Assessment Questions (SAQs) for Session 11 .............................................................................. 113
Study SessionTwelve: Resource Allocation/Assignment: .......................................................... 115
(Vogel’s Approximation Method) .............................................................................................. 115
Introduction ........................................................................................................................................... 115
Learning Outcomes for Study Session 12 ............................................................................................. 115
12.1. Vogel’s Approximation Method in Resource Allocation ............................................................ 115
Summary ofSession 12 ......................................................................................................................... 119
Self-Assessment Questions (SAQs) for Session 12 .............................................................................. 120
References ............................................................................................................................................. 121
Study Session Thirteen: Model in Education.............................................................................. 122
Introduction ........................................................................................................................................... 122
Learning Outcomes for Study Session 13 ............................................................................................. 122
13.1. Meaning of a Model ..................................................................................................................... 123
13.2.DerivingSolutionsfromModels...................................................................................................... 127
13.2.1. Testing the Model and the Solution ...................................................................................... 127
13.3. Model Building Process ............................................................................................................... 130
13.4. Lewin’s Change Management Model .......................................................................................... 131
13.5. McKinsey 7-S Model ................................................................................................................... 132
13.5.1. The Benefits of McKinsey 7-S Model .............................................................................. 133
13.5.2. The Disadvantages of McKinsey 7-S Model are: ................................................................. 133
13.6. Kotter’s 8 Step Change Model ..................................................................................................... 134
13.6.1. Advantages of Kotter’s 8 Step Change Model ...................................................................... 135
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13.6.2. Disadvantages of Kotter’s 8 Step Change Model ................................................................. 135
Summary of Session 13 ........................................................................................................................ 135
Self-Assessment Questions (SAQs) for Session 13 .............................................................................. 136
References ............................................................................................................................................. 138
Study SessionFourteen: Decision Making Process: PPBS ......................................................... 139
Introduction ........................................................................................................................................... 139
Learning Outcomes for Study Session 14 ............................................................................................. 139
14.1. Meaning of Decision Making and Types of Decisions ................................................................ 139
14.1.1. Meaning of Decision Making ............................................................................................... 140
14.1.2. Types of Decisions .................................................................................................................... 141
14.2. Planning, Programming, Budgeting System (PPBS) ................................................................... 141
14.2.1. Decision-Making under states of Certainty, Uncertainty and Risk ....................................... 142
14.2.2. Proactive and Reactive Decisions ......................................................................................... 142
14.2.3. The Rational Decision Making Process ................................................................................ 143
14.2.4. Individual Decision Making .................................................................................................. 145
14.2.5. A Group Decision-Making .................................................................................................... 146
14.3. Decision Making Techniques....................................................................................................... 148
14.3.1. Brainstorming ....................................................................................................................... 149
14.3.2. The Delphi Technique ........................................................................................................... 149
14.3.3. The Nominal Group Technique (NGT) ................................................................................. 150
14.3.4. Marginal Analysis ................................................................................................................. 150
14.3.5. Cost Benefit or Cost Effectiveness Analysis ........................................................................ 151
14.3.6. Decision Trees....................................................................................................................... 151
Summary of Unit 14 .............................................................................................................................. 153
Self-Assessment Questions (SAQs) for Session 14 .............................................................................. 154
References ............................................................................................................................................. 155
Study Session Fifteen: Management by Objectives (MBO) ....................................................... 156
Introduction ........................................................................................................................................... 156
Learning Outcomes for Study Session 15 ............................................................................................. 156
15.1. Meaning, Strengths and Weaknesses of Management by Objectives .......................................... 156
15.1.1. Meaning of Management by Objectives ............................................................................... 156
15.1.2. Strengths of Management by Objectives .............................................................................. 159
15.1.3. Weaknesses of Management by Objectives .......................................................................... 159
15.2. Activities in Management by Objectives (MBO) ........................................................................ 160
Summary of Session 15 ........................................................................................................................ 162
Self-Assessment Questions (SAQs) for Session 15 .............................................................................. 163
References ............................................................................................................................................. 164
Study Session Sixteen: Linear Programming ............................................................................. 165
Introduction ........................................................................................................................................... 165
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Learning Outcomes for Study Session 16 ............................................................................................. 165
16.1. Meaning, Formulation, and Structureof Linear Programming ..................................................... 165
16.1.1. Meaning of Linear Programming .......................................................................................... 165
16.1.2. Formulation of the Linear Programming Problem ................................................................ 169
16.1.3. Structure of Linear Programming model .............................................................................. 170
16.2. Assumptions of Linear Programming Certainty .......................................................................... 171
16.2.1. General Mathematical Model of an LPP ............................................................................... 171
16.2.2. Guidelines for Formulating Linear Programming Model ..................................................... 172
Summary of Session 16 ........................................................................................................................ 173
Self-Assessment Questions (SAQs) for Session 16 .............................................................................. 174
References ............................................................................................................................................. 175
APPENDIX ........................................................................................................................................... 176
Notes to the Self-Assessment Questions (SAQs) for Session 1 ............................................................ 176
Notes to the Self-Assessment Questions (SAQs) for Session 2 ............................................................ 176
Notes to the Self-Assessment Questions (SAQs) for Session 3 ............................................................ 177
Notes to the Self-Assessment Questions (SAQs) for Session 4 ............................................................ 178
Notes to the Self-Assessment Questions (SAQs) for Session 5 ............................................................ 179
Notes to the Self-Assessment Questions (SAQs) for Session 6 ............................................................ 180
Notes to the Self-Assessment Questions (SAQs) for Session 7 ............................................................ 180
Notes to the Self-Assessment Questions (SAQs) for Session 8 ............................................................ 182
Notes to the Self-Assessment Questions (SAQs) for Session 9 ............................................................ 183
Notes to the Self-Assessment Questions (SAQs) for Session 10 .......................................................... 184
Notes to the Self-Assessment Questions (SAQs) for Session 11 .......................................................... 184
Notes to the Self-Assessment Questions (SAQs) for Session 12 .......................................................... 185
Notes to the Self-Assessment Questions (SAQs) for Session 13 .......................................................... 185
Notes to the Self-Assessment Questions (SAQs) for Session 14 .......................................................... 187
Notes to the Self-Assessment Questions (SAQs) for Session 15 .......................................................... 188
Notes to the Self-Assessment Questions (SAQs) for Session 16 .......................................................... 189
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Course Overview
Operations Management in Educational Practice (EME 302) is a course that has been
designed for your understanding of the concept. In defining Operations Management, it
deals with the application of scientific methods to the management and administration of
organizations such as: education, military, governmental, commercial, and industrial
processes. It has the basic aspects as operations research which attempts to provide those
who manage organized systems with an objective and quantitative basis for
decision.Operations research is not a science itself but rather the application of science to
the solution of managerial and administrative problems. You also need to note that this
course focuses on the performance of organized systems treated wholly. It is usually
concerned with systems in which human behaviour plays an important part. Operations
research was originally concerned with improving the operations of existing systems
rather than developing new ones.The subject matter consists of decisions that control the
operations of systems. Hence, it is concerned with how managerial decisions are and
should be made, how to acquire and process data and information required to make
decisions effectively, how to monitor decisions once they are implemented, and how to
organize the decision-making and decision-implementation process. Extensive use is
made of older disciplines such as logic, mathematics, andstatistics, as well as more recent
scientific developments such as communications theory, decision theory, cybernetics,
organization theory, the behavioral sciences, and general systems theory. Owing to the
complexities of the educational system, operation Management becomes an important
instrument for achieving efficiency in the system, hence the need for you to pay a rapt
attention as you go through the lectures in this course.
Course Objectives
This course is aimed at intimating you with the following:
1. The roots from which modern management sprang.
2. The principles which guide human behaviour and performance organizations with
special reference to educational institutions; and
3. Techniques which are available to the managers in the absence of an enabling
environment.
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Study Session One The Development of Modern Management
Principles
Expected duration: 1 week or 2 contact hours
Introduction
I’m welcoming you to the first lecture in EME 302 which will be focusing on how
modern management principles evolved. You would agree with me that we are all born in
an organisation (a family), we live in organisations (society) and at the same time work in
organizations (Business, Government, Army, School, College etc.). Each one of these
organisations is a group of persons working together to achieve some common
objectives. The organisations can be successful only when the efforts of various
individuals in the groups are integrated into team work. The central agency which
performs this task is known as management. Another interesting thing you need to note is
that management plays the same role in an organization as the brain does in human body.
All these activities are what sums up in the development of modern management
principles as it would be treated in this lecture.
Learning Outcomes for Study Session 1
At the end of this lecture, it is expected that you will be able to;
1.1. Define and use correctly keywords printed in bold. (SAQ 1.1.)
1.2. Examine a fair background of management practice as dating back to
creation of man. (SAQ 1.2)
1.3. Discuss briefly on how the study of management began.(SAQ 1.3)
1.4. Highlight the major activities that stemmed from modern management era.
(SAQ 1.4)
Key words: management and civilization
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1.1. The Origin and Evolution of Management
1.1.1. Origin of Management
As you would expect, many records and ideas relating to management date from
antiquity. Managementhas been practiced in some form or the other since the dawn of
civilisation. Ever since human beings began to live and work together in groups,
techniques of organisation and management were evolved. The pyramids of Egypt, the
Chinese civil service, the Roman Catholic Church, and military organisation offer good
examples of the application of management in ancient times. Kawtilya’s Arthashashtra,
the Bhagwat Gita, the Holy Bible and other epics contain referencesto the management of
public affairs. The early contributions to management thought came from Roman
Catholic Church, Military organizations and camera-lists. Thus, art of management has
ancient origins.
However, the science of management developed largely after the industrial Revolution
which established the factory system. Scientific Management movement laid the
foundations of Management as a science.Modern Management thought has developed
during several stages. These stages, approaches or theories to the study of Management
can be classified as follows;
1. Classical theory
2. Neo-classical theory
3. Modern Theory
Teachers are the only professionals who, like managers, are perceived on two
dimensions. To be an educational manager (manager and teacher) which therefore
subjects one to double scrutiny. In the early century, Frederick Taylor popularised the
word 'management' to describe what he had formerly and more accurately called 'work
study' or 'task study'. That aspect of management is referred to today as Industrial
Engineering. It is important for you to note that Management as a practice is not new as it
dates back to creation as every man organizes personal affairs to attain desired ends.
However, as societies became complex, there was need for harmonization of affairs to
achieve desired goals. The impact of the work of managers is felt in the development and
progress that is noticeable within the societies, groups, organizations, units, etc. This
applies to a family, a company or a nation. However, this can be linked to planning,
3
organizing, deciding and implementing as Drucker (1974) observed that:
"Our society has become, within an incredibly short fifty year, a society of
institutions. It has become a pluralistic society in which every major social
task has been entrusted to large organizations - from producing economic
goods and services to health care, from social security and welfare to
education, from the search for new knowledge to the protection of the
natural environment ..., (and) it is the managers and management that
make institutions perform."
In addition to that, the degree of success attained by any society, group or organization
depends on the quality of it; administrators/managers. For management to make a
difference, three criteria must be fulfilled namely, goals, people and other resources.
While goals must be specified in quantifiable terms, resources must be limited to
necessitate efficiency of use and the people must not only be efficient and effective but
also reliable.
In-text Question
• What are those activities that offer good examples of the application of
management in ancient times?
• Such activities are; the pyramids of Egypt, the Chinese civil service, the Roman
Catholic Church, and military organization.
1.1.2. The Evolution of Management
This is another phase in this lecture which will be addressing the evolution of
Management. Management thinking and practice have evolved over the last century
because of increased understanding of human and organisational behaviour, the economic
climate and historical context and the changes in generations over time. However, if you
will be honest, you would observe that much of what we practice today is due to the
consulting industry playing on executives’ fears and aspirations by selling products and
services that cause more problems than solutions, and our own human weakness of
always looking for a quick fix even to very complex issues. It is time to rethink
Management. But before we do that, let’s take a look at the rear-view mirror and see how
4
we got to where we are today with the aid of Fig 1.1.
Fig 1.1. The various trends in the Evolution of Management
Image source: http://www.bmmagazine.co.uk/in-business/advice/the-evolution-of-management/
From Fig 1.1.
1. Management Approach: the style of top management, ranging from:
a. Control (i.e. your line manager tells you what to do and how to do it).
b. Set Goals (i.e. your line manager sets goals and expectations, but you have more
freedom with regards to how you achieve them).
c. Inspire (i.e. your line manager gives you scope and freedom to innovate on both
the what and the how).
2. Approach to Innovation/Problem Solving: how leaders solve strategic problems and
develop new products and services. This ranged from:
a. Top Down (i.e. solutions are created and come from the top)
b. Top Down with Bottom Up Data (i.e. the rest of the organisation contributes
information and experiences, but solutions are still created at the top).
5
c. Participatory (i.e. solutions are created collaboratively, and throughout the
organisational levels).
After a century of trying to control people, processes and information, we have come to a
point in organisational history where we need to recognise that what worked before just
simply is not enough anymore. Traditional Management is fine if you want compliance,
but if you want innovation and growth, you need to engage your people on a whole new
level. Top down control is a thing of the past. Succeeding in today’s environment
requires a management style that inspires and is participatory.
Now let us have a look at each of these successive periods;
a. 1910s-1940s: Management as Science
As seen in the top down level of Fig 1.1. management as Science was developed in the
early 19th century and focused on increasing productivity and efficiency through
standardisation, division of labour, centralisation and hierarchy. A very ‘top down’
management with strict control over people and processes dominated across industries.
b. 1950s-1960s: Functional Organisations
Due to growing and more complex organisations, the 1950’s and 1960’s as seen in Fig
1.1. saw the emergence of functional organisations and the Human Resource (HR)
movement. Managers began to understand the human factor in production and
productivity and tools such as goal setting, performance reviews and job descriptions
were born.
In-text Question
• You have observed that Bola who is your line manager at work always does the
following a tells you what to do and how to do it, sets goals and expectations, but
gives you scope and freedom to innovate on both the what and the how. What
approach do you think he is using?
• Clearly he is using the Management Approach: the style of top management, ranging
from: a. Control, goal setting and inspiration.
c. 1970s: Strategic Planning
6
As we proceed in our discussion on evolution of management, another stage we need to
consider is the strategic planning of the 1970s. During this period, the focus was changed
from measuring function to resource allocation and tools like Strategic Planning (GE),
Growth Share Matrix (BCG) and SWOT were used to formalise strategic planning
processes. After several decades of ‘best practice’ and ‘one size fits all’ solutions,
academics began the development of contingency theories.
d. 1980s: Competitive Advantage
As the business environment grew increasingly competitive and connected, and with a
blooming management consultancy industry, Competitive Advantage became a priority
for organisations in the 1980’s. Tools like Total Quality Management (TQM), Six Sigma
and Lean were used to measure processes and improve productivity. Employees were
more involved by collecting data, but decisions were still made at the top, and goals were
used to manage people and maintain control.
e. 1990s: Process Optimisation
Benchmarking and business process reengineering became popular in the 1990’s, and by
the middle of the decade, 60% of Fortune 500 companies claimed to have plans for or
have already initiated such projects. TQM, Six Sigma and Lean remained popular and a
more holistic, organisation-wide approach and strategy implementation took the stage
with tools such as Strategy Maps and Balance Scorecards.
f. 2000s: Big Data
Looking at the present state as presented on Fig 1.1., this era is largely driven by the
consulting industry under the banner of Big Data, organisations in the 2000’s started to
focus on using technology for growth and value creation. Meanwhile, oversaturation of
existing market space drove to concepts such as Blue Ocean Strategy and Value
Innovation. You also need to note that globalisation, advances in technology, and
increased diversity have put organisational challenges into hyper drive. Despite the
inspirational stories we read about companies like Zappos, Innocent Drinks and Google,
the truth is that most of us are using out-dated management practices and failing to get
the most out of our people. How we lead our people and how we solve problems and
innovate, are some of the most important aspects of Management to get right. Through
7
research, we have therefore looked specifically at two aspects of Management throughout
history, and how these will develop in the future.
Box 1.1. Stages in the Evolution of Management
The stages in the evolution of Management are;
1. Management as a science (1910s-1940s)
2. Functional organisations (1950s-1960s)
3. Strategic planning (1970s)
4. Competitive advantage (1980s)
5. Process optimization (1990s)
6. Big data (2000s)
1.2. Modern Management Era
1.2.1. Empirical School
As the heading suggests, this relates to the current Management Era. Ernest Dale, the
founder of this school, identified management as a study of experience. The intention of
studying experience is to draw generalizations and to develop means of teaching
experiences to other practitioners and students. As such, it is also called the case
approach or management experience approach. The unique features of this school are as
follows:
1. Managerial experience can be passed from one person to another.
2. Management can be taught best by the case method.
3. Theories of management can be developed by studying many experiences.
4. It is a study of success and failures in the application of management techniques
by managers in their practice.
Although the case method helps in developing diagnostic and analytical skills in
management students in classroom situations, it may not be useful in dynamic situations.
1.2.2. SocialSchool System
The social school system stems from the application of behavioural sciences to
management. Vilfredo Pareto, a sociologist is the real pioneer of the social system, i.e. a
system of cultural interrelationship. His ideas were later developed by Chester Barnard
who is regarded as the founding father of the social system school. For the adherents of
8
this school, an organization is essentially a socio-cultural system composed of groups of
people who work in cooperation with one another.
The broad features of this school are as follows:
1. An organization is a social system-a system of cultural relationship.
2. Relationships exist among the external and internal environments of the organization.
3. Cooperation among group members is necessary for the achievement of
organizational objectives.
4. For effective management, efforts should be made for establishing harmony between
the goals of the organization and the various groups functioning therein.
Barnard in his famous book, The Functions of an Executive, has identified the following
three types of functions of an executive. These are;
1. Maintenance of organizational communication through formal interaction.
2. Achieving organizational purpose by securing essential services from individuals in
the organization.
3. Formulation and definition of the organizational purpose.
Barnard has also given a new concept of authority known as the acceptance theory of
authority. In his opinion, a person will accept authority only when the following four
conditions are met simultaneously.
You can pause to consider these conditions;
1. He can understand the communication.
2. He believes that it is consistent with the organizational purpose.
3. He believes it to be compatible with his own personal interests.
4. He is mentally and physically able to comply with it.
The concept of informal organization is also a contribution of this school. The supporters
of this school advocate that efforts should be directed towards establishing harmony
between the goals of the organization and the goals of the groups and individual
members.
9
1.2.3. Decision Theory School
In another trend in modern management, Herbert Simon, Luther Gulick and Lyndall
Urwick are the major contributors to this school of thought. Decision theory concentrates
on rational approaches to decision making-the selection of a course of action from
various possible alternatives. The manager is a decision maker and the organization is a
decision-making unit. Hence the basic problem in managing is to make rational decisions.
The main features of this theory are as follows:
1. Decision making is central to the study of management.
2. The members of the organization are decision makers and problem solvers. Thus,
management is the study of the process of decision-making and the personalities
and behaviour of the decision makers.
3. The organizational effectiveness depends on the quality of decisions.
4. All factors affecting decision making are the subject matter of the study of
management.
Although the decision theory school contributes to the sharpening of managerial tools
especially for making suitable decisions in the organization, it does not take the total
view of management. As such, its scope is quite limited considering the requirements of
management. Decision-making is significant in every school of management. This
significant aspect cannot be denied, but management is more than mere decision making.
Activity 1.1. Time Allowed: 1hour
Take a moment to reflect on what you have learnt on modern management era and
highlight at least one significant activity under each era.
Activity 1.1. Feedback
1. The Empirical School: Studying experience to draw generalizations and to develop
means of teaching experiences to other practitioners and students.
2. The Social School System: This stems from the application of behavioural
sciences to management.
3. The Decision Theory School: This concentrates on rational approaches to decision
making-the selection of a course of action from various possible alternatives.
10
Summary of Session 1
In this Session, you have learned that;
1. Management has been practiced in some form or the other since the dawn of
civilisation. Ever since human beings began to live and work together in groups,
techniques of organisation and management were evolved.
2. The science of management developed largely after the industrial Revolution
which established the factory system.
3. Modern Management thought has developed during several stages. These stages or
approaches may be classified as; Classical theory; Neo-classical theory and
Modern Theory.
4. For management to make a difference, three criteria must be fulfilled namely,
goals, people and other resources. While goals must be specified in quantifiable
terms, resources must be limited to necessitate efficiency of use and the people
must not only be efficient and effective but also reliable.
5. Management thinking and practice have evolved over the last century because of
increased understanding of human and organisational behaviour, the economic
climate and historical context and the changes in generations over time.
6. In the evolution of management, there are stages involved. We have management
as a science (1910-1940); functional organisations (1950-1960); strategic planning
(1970s); competitive advantage (1980s); process optimization(1990s); and big data
(2000s).
7. In modern management era, we have; empirical school; social school system; and
decision theory school.
Self-Assessment Questions (SAQs) for Session 1
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 1.1. (tests learning outcome 1.1.)
Identify the TRUE/FALSE statements from the items provided below;
a. Managementhas been practiced in some form or the other since the dawn of
civilisation.
11
b. The science of management developed largely before the industrial Revolution
which established the factory system.
SAQ 1.2. (tests learning outcome 1.2.)
Describe the origin of management in relation to the creation of man.
SAQ 1.3. (tests learning outcome 1.3.)
In tracing the evolution of management, what major activity will you attribute to its
turnaround?
SAQ 1.4. (tests learning outcome 1.4.)
Based on what you have learnt in this lecture, what are the major activities dominating
the modern management era.
References
Bach, Stephen & Sisson, Keith (ed.) (2000); Personnel Management: A comprehensive
guide to theory and practice, Blackwell Business, Oxford.
Drucker, P. (1974): Management: Tasks, Responsibilities, Practices. New York: Harper
and Row.
George Jr, C.S. (1972): The History of Management Thought. Englewood Cliffs: Prentice
Hall
12
Study Session Two: Programme Evaluation and Review Technique
(PERT)
Expected duration: 1 week or 2 contact hours
Introduction
Welcome to another lecture in EME 302. This lecture is meant to acquaint you with the
programme evaluation review technique(PERT). You need to understand that managers
can obtain a great deal of information by analyzing network diagrams of projects. For
example, network diagrams show the sequence of activities involved in a project. From
this sequence, managers can determine which activities must take place before others can
begin and which can occur independently of one another. Managers can also gain
valuable insight by examining paths other than the critical path. Since these paths require
less time to complete, they can often accommodate slippage without affecting the project
completion time. The difference between the length of a given path and the length of the
critical path is known as slack. Knowing where slack is located helps managers to
allocate scarce resources and direct their efforts to control activities. Your attention is
needed to assimilate the contents of this lecture.
Learning Outcomes for Study Session 2
At the end of this lecture, it is expected that you will be able to;
2.1. Define and use correctly keywords printed in bold. (SAQ 2.1.)
2.2. Describe Program Evaluation Review Technique. (SAQ 2.2.)
2.3. Identify the steps involved in PERT planning.(SAQ 2.3.)
2.4. Outline project information input in PERT analysis. (SAQ 2.4)
Key words;evaluate, estimate, cost, time, planning, and coordinating.
2.1. Meaning and Analysis of Program Evaluation and Review Technique (PERT)
2.1.1. Meaning of Program Evaluation and Review Technique
Program Evaluation and Review Technique (PERT) is a technique adopted by
organizations to analyze and represent the activity in a project and to illustrate the flow of
13
events in a project. PERT is a method to evaluate and estimate the time required to
complete a task within deadlines. PERT serves as a management tool to analyze, define
and integrate events. PERT also illustrates the activities and interdependencies in a
project. The main goal of PERT is to reduce the cost and time needed to complete a
project.
This technique is a widely-used method for planning and coordinating large-scale
projects. As Harold Kerzner explained in his book Project Management, "PERT is
basically a management planning and control tool. It can be considered as a road map for
a program or project in which all the major elements (events) have been completely
identified, together with their corresponding interrelations'. You need to note that PERT
charts are often constructed from back to front because for many projects, the end date is
fixed and the contractor has front-end flexibility." A basic element of PERT-style
planning is to identify critical activities on which others depend. The technique is often
referred to as PERT/CPM, the CPM standing for "critical path method."
Let us briefly discuss the history of PERT, it was known to be developed during the
1950s through the efforts of the U.S. Navy and some of its contractors working on the
Polaris missile project. Concerned about the growing nuclear arsenal of the Soviet Union,
the U.S. government wanted to complete the Polaris project as quickly as possible. The
Navy used PERT to coordinate the efforts of some 3,000 contractors involved with the
project. Experts credited PERT with shortening the project duration by two years. Since
then, all government contractors have been required to use PERT or a similar project
analysis technique for all major government contracts. PERT was developed in 1950 by
the U.S. Navy during the Cold War and is intended for large projects, which are;
1. complex;
2. require a series of sequential tasks; and
3. performed in parallel with other projects.
Before we discuss PERT analysis, let us consider the steps in PERT planning.
Steps in PERT planning are;
14
• Identifying Tasks and Milestones: Every project involves a series of required
tasks. These tasks are listed in a table allowing additional information on sequence
and timing to be added later.
• Placing the Tasks in a Proper Sequence: The tasks are analyzed and placed in a
sequence to get the desired results.
• Network Diagramming: A network diagram is drawn using the activity sequence
data showing the sequence of serial and parallel activities.
• Time Estimating: This is the time required to carry out each activity, in three parts:
o Optimistic timing: The shortest time to complete an activity.
o Most likely timing: The completion time having the highest probability.
o Pessimistic timing: The longest time to complete an activity
• Critical Path Estimating: This determines the total time required to complete a
project.
Box 2.1. Program Evaluation and Review Technique
Please note these points;
• PERT is widely-used method for planning and coordinating large-scale projects.
• A basic element of PERT-style planning is to identify critical activities on which others depend.
• The technique is often referred to as PERT/CPM, the CPM standing for "critical path method."
• PERT was developed during the 1950s through the efforts of the U.S. Navy and some of its contractors
working on the Polaris missile project.
To round up this discussion on meaning of PERT, it is important for you to know that it
does not only determines the time to complete a specific software development activity,
but also determines the cost.PERT is a project managementtechnique that shows the time
taken by each component of a project, and the total time required for its completion.
PERT breaks down the project into events and activities, and lays down their proper
sequence, relationships, and duration in the form of a network. Lines connecting the
events are calledpaths, and the longest path resulting from connecting all events is called
the critical path. The length (duration) of the critical path is the duration of the project,
and any delay occurring along it delays the whole project. PERT is a schedulingtool, and
does not help in finding the best or the shortest way to complete a project.
15
In-text Question
• A team of school owners have come together to carry out a project they have
decided that the best way to accomplish this task is using PERT. So far, they have
carried out two steps in the entire process. They have identified tsks and
Milestones in a table. They have also gone ahead to place the tasks in a proper
sequence. Explain to them the next two steps under the PERT that they will have
to carry out.
o The next two steps are Network Diagramming and Time Estimating:
o When creating a network diagram they will use the activity sequence data
showing the sequence of serial and parallel activities. Timing estimating
involves the time required to carry out each activity, in three part.
2.1.2. Pert Analysis
We have come to another concept under PERT and this is PERT analysis. For complex
problems involving hundreds of activities, computers are used to create and analyze the
project networks. The project information input into the computer includes; the earliest
start time for each activity; earliest finish time for each activity; latest start time for each
activity; and latest finish time for each activity without delaying the project completion.
From these values, a computer algorithm can determine the expected project duration and
the activities located on the critical path. Managers can use this information to determine
where project time can be shortened by injecting additional resources, like workers or
equipment. Nonetheless, the solution of the algorithm is easy for the computer, but the
resulting information will only be as good as the estimates originally made. Thus, PERT
depends on good estimates and sometimes inspired guesses.
PERT offers several advantages and disadvantages to managers. Some of the advantages
are;
1. It forces them to organize and quantify project information and provides them with
a graphic display of the project.
2. It also helps them to identify which activities are critical to the project completion
time and should be watched closely, and which activities involve slack time and
can be delayed without affecting the project completion time.
16
Despite these advantages, you also need to note that this technique is posed with some
limitations which are;
1. Complex systems and plans, with many suppliers and channels of supply involved,
sometimes make it difficult to predict precisely what will happen.
2. The technique works best in well-understood projects where sufficient experience
exists to predict tasks accurately in advance.
Activity 2.1. Time Allowed: 1 hour
Get a cardboard paper and map out PERT planning steps in a hierarchical order.
Activity 2.1. Feedback
Your sketch should follow this order; Identifying tasks and milestones; Placing the tasks
in a proper sequence; Network diagramming; Time estimating and Critical Path
estimating.
2.2. Critical Path Analysis, and Critical Path Method
As seen in Fig 2.1, the critical path analysis, method is a network map of a project,
tracing the work from a departure point to the completion objective.
Fig 2.1. Critical Path Analysis and Critical Path Method
Image source: http://www.ifm.eng.cam.ac.uk/research/dstools/critical-path-analysis/
Using Fig 2.1., any activity is represented by a line or arrow. This line or arrow connects
two events. Each event is a specific point in time, marking the beginning and/or end of an
activity.Artificial dummy events may be included to ensure that all activities have a
unique pair of event numbers. Also, network dummy activities, (shown by dashed line)
17
which take no time but indicate dependence. Dummies are particularly necessary in
computerised CPMs.The network may also include time/calendar information (including
boundaries) and hence deadline data.
Summary of Session 2
In this Session, you have learned that;
1. Program Evaluation and Review Technique (PERT) is a technique adopted by
organizations to analyze and represent the activity in a project and to illustrate the
flow of events in a project.
2. PERT was developed during the 1950s through the efforts of the U.S. Navy and
some of its contractors working on the Polaris missile project.
3. PERT is a project managementtechnique that shows the time taken by each
component of a project, and the total time required for its completion.
4. PERT breaks down the project into events and activities, and lays down their
proper sequence, relationships, and duration in the form of a network. Lines
connecting the events are calledpaths, and the longest path resulting from
connecting all events is called the critical path.
5. The length (duration) of the critical path is the duration of the project, and any
delay occurring along it delays the whole project.
6. PERT is a schedulingtool, and does not help in finding the best or the shortest way
to complete a project.
7. PERT planning steps are: Identifying Tasks and Milestones, Placing the Tasks in a
Proper Sequence, Network Diagramming, Time Estimating and Critical Path
Estimating.
Self-Assessment Questions (SAQs) for Session 2
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 2.1. (tests learning outcome 2.1.)
Fill in the blanks in the sentences provided below using the appropriate keywords.
a. PERT is a method to _________ and ________ the time required to complete a
task within deadlines.
18
b. The main goal of PERT is to reduce the _______ and _______ needed to complete
a project.
c. PERT is widely-used method for _________ and ________ large-scale projects.
SAQ 2.2. (tests learning outcome 2.2.)
Based on the knowledge you have gained in this lecture; how would you describe PERT
if you are called upon to do so?
SAQ 2.3. (tests learning outcome 2.3.)
As an expert in Educational Management, you have been given a project by the Ministry
of Education. In deciding on the technique to use, you have adopted PERT. What are the
steps that will guide you in having an effective planning for your chosen technique?
SAQ 2.4. (tests learning outcome 2.4.)
In the conduct of PERT analysis, make a list of project information inputs that are needed
for the analysis result.
References
Harold Kerzner 2003. Project Management: A Systems Approach to Planning,
Scheduling, and Controlling (8th Ed. ed.). Wiley. ISBN 0-471-22577-0.
Milosevic, Dragan Z. 2003. Project Management ToolBox: Tools and Techniques for the
Practicing Project Manager. Wiley. ISBN 978-0-471-20822-8.
Project Management Institute 2013. A Guide to the Project Management Body of
Knowledge (5th ed.). Project Management Institute. ISBN 978-1-935589-67-9.
19
Study Session Three: Critical Path Method (CPM)
Expected duration: 1 week or 2 contact hours
Introduction
In the last lecture, critical path method was briefly mentioned and it is also a major
approach in PERT. However, this lecture is meant to dwell more on it. Before we go into
the content of this lecture, you need to know that project schedule plan is the main plan
included in any Project Management Plan. Project schedule is responsible for bringing
project time, cost and quality under control. Project schedule links resources, tasks and
time line together. Once a project manager has list of resources, work breakdown
structure (WBS) and effort estimates, it is good to go for planning project schedule.
Schedule network analysis helps project manager to prevent undesirable risks involved in
the project. This brings us to the business of this lecture which is the Critical Path
Method (CPM) and Critical Chain Project Management (CCPM) which are key elements
of schedule network analysis.
Learning Outcomes for StudySession 3
At the end of this lecture, it is expected that you will be able to;
3.1. Define and use correctly keywords printed in bold. (SAQ 3.1.)
3.2. Describe the Critical Path Method used for projects. (SAQ 3.2)
3.3. Identify the 6 key steps in Critical Path Method. (SAQ 3.3.)
3.4. Highlight at least 3 merit and demerits each of CPM (SAQ 3.4)
3.5. Pinpoint the relevance of CCPM to CPM. (SAQ 3.5)
Key words; planning, scheduling, controlling, and float time
20
3.1. Meaning, Steps, and Merits, and Demerits of Critical Path Method (CPM)
3.1.1. Meaning of Critical Path Method
CPM is a method for planning, scheduling, and controlling projects.The critical path
method (CPM) is a step-by-step technique for process planning that defines critical and
non-critical tasks with the goal of preventing time-frame problems and process
bottlenecks. The CPM is ideally suited to projects consisting of numerous activities that
interact in a complex manner.
In applying the CPM, there are several steps that can be summarized as follows:
a. define the required tasks and put them down in an ordered (sequenced) list.
b. create a flowchart or other diagram showing each task in relation to the others.
c. identify the critical and non-critical relationships (paths) among tasks.
d. determine the expected completion or execution time for each task.
e. locate or devise alternatives (backups) for the most critical paths.
CPM was developed in the 1950s by DuPont, and was first used in missile-defense
construction projects. Since that time, CPM has been adapted to other fields including
hardware and software product research and development. Various computer programs
are available to help project managers use the CPM.CPM is based on mathematical
calculations and it is used for scheduling project activities. The initial critical path
method was used for managing plant maintenance projects. Although the original method
was developed for construction work, this method can be used for any project where
there are interdependent activities. In the critical path method, the critical activities of a
program or a project are identified. These are the activities that have a direct impact on
the completion date of the project. The Critical Path Method (CPM) is a schedule
network analysis technique.Critical path determines the shortest time to complete the
project and it is the longest duration path through a network of tasks.
In-text Question
• A group of educational experts decided to come together to carry out a project in a
community the project is to last for 3months. The project centers on carrying out
adult education in a small rural community. They have decided to use CPM as
21
their approach to managing the project. Do you think this is a good choice of
method? State why
o Well, the CPM is not really the best choice of method for this project because,
CPM is ideally suited to projects consisting of numerous activities that interact
in a complex manner. There are several other approaches that can be adopted
to suit a project like this which we shall discuss as we go along.
Another important point which is crucial here is that critical tasks (activities) are tasks
(activities) on the critical path. To understand CPM further, the first thing is to
understand the nature of the task. Using the standard laid by Project Management Body
of Knowledge (PMBOK), every scheduled task can be defined by the following four
parameters.
a. Early Start (ES): Earliest possible point in time on which a task can start.
b. Early Finish (EF): Earliest possible point in time on which a task can finish.
c. Late Start (LS): Latest possible point in time on which a task can start.
d. Late Finish (LF): Latest possible point in time on which a task can finish.
Let us continue our discussion on The CPM. Early Start and finish dates are calculated by
means of Forward Pass; Late Start; and Late Finish dates are calculated by means of
Backward Pass. Many Tasks have some amount of buffer added to them referred as Slack
Time or Float. Float time is amount of time a task can sleep before it delays project
schedule. There are two common types of floats.
• Free Float: Amount of time a single task can be delayed without delaying the
early start of any successor task.
• Total Float: Amount of time a single task can be delayed without delaying project
completion.
Mathematically Float is defined as: Float = LS - ES or LF - EF. Critical path has zero or
negative Total Float. A project can have several critical paths.
In-text Question
• In the critical path method, how would you describe the critical activities of a
program or a project?
22
o These are the activities that have a direct impact on the completion date of the
project.
Fig 3.1 Shows an example of how the CPM is charted.
Figure 3.1: An example of CPM
Image source: http://www.pcoder.net/cpm-a-tough-example/#axzz4O62ADMCi
3.1.2. Key Steps in Critical Path Method
Let us have a look at how critical path method is used in practice with reference to Fig
3.1. The process of using critical path method in project planning phase has six steps. We
have;
Step 1: Activity specification
This is the first step in critical path method. You can use the Work Breakdown Structure
(WBS) to identify the activities involved in the project. This is the main input for the
critical path method. In activity specification, only the higher-level activities are selected
for critical path method. When detailed activities are used, the critical path method may
become too complex to manage and maintain.
23
Step 2: Activity sequence establishment
In this step, the correct activity sequence is established. For that, you need to ask three
questions for each task of your list.Pause to consider these questions;
i. Which tasks should take place before this task happens.
ii. Which tasks should be completed at the same time as this task.
iii. Which tasks should happen immediately after this task.
Step 3: Network diagram
Once the activity sequence is correctly identified, the network diagram can be drawn
(Figure 3.1). Although this diagram was drawn, there are several computer softwares,
such as Primavera that is being used for this purpose nowadays.
Step 4: Estimates for each activity
This could be a direct input from the WBS based estimation sheet. Most organisations
use 3-point estimation method or COCOMO based (function points based) estimation
methods for tasks estimation. You can use such estimation information for this step of the
process.
Step 5: Identification of the critical path
For this, you need to determine four parameters of each activity of the network. These
parameters are;
i. Earliest start time (ES) - The earliest time an activity can start once the previous
dependent activities are over.
ii. Earliest finish time (EF) - ES + activity duration.
iii. Latest finish time (LF) - The latest time an activity can finish without delaying the
project.
iv. Latest start time (LS) - LF - activity duration.
The float time for an activity is the time between the earliest (ES) and the latest (LS) start
time or between the earliest (EF) and latest (LF) finish times. During the float time, an
activity can be delayed without delaying the project finish date. The critical path is the
longest path of the network diagram. The activities in the critical path influence the
24
deadline of the project. If an activity of this path is delayed, the project will be delayed.
In case if the project management needs to accelerate the project, the times for critical
path activities should be reduced.
Step 6: Critical path diagram to show project progresses
This is known as the last step in CPM. Under this step, critical path diagram is a live
artifact. Therefore, this diagram should be updated with actual values once the task is
completed. This gives more realistic figure for the deadline and the project management
can know whether they are on track regarding the deliverables.
Box 3.1. Key steps in Critical Path Method
The key steps in critical path method are;
1. Activity specification
2. Activity sequence establishment
3. Network diagram
4. Estimates for each activity
5. Identification of the critical path; and
6. Critical path diagram to show project progresses.
3.1.3 Merits of Critical Path Method
Let us consider the following merits of Critical Path Method. We have;
i. Offers a visual representation of the project activities.
ii. Presents the time to complete the tasks and the overall project.
iii. Tracking of critical activities.
In the same vein, CPM is also helpful in:
a. Project Planning and control.
b. Time-cost trade-offs.
c. Cost-benefit analysis.
d. Contingency planning.
e. Reducing risk.
25
3.1.4 Demerits of Critical Path Method
Despite the advantages of CPM, it is also faced with the following limitations;
a. CPM assumes low uncertainty in schedule dates.
b. Does not consider resource dependencies.
c. Less efficient use of buffer time.
d. Less focus on non-critical tasks that can cause risk.
e. Based on only deterministic task duration.
f. Critical Path can change during execution.
Activity 3.1.
Select an educational project on your own and make a list of the steps you would embark
on in applying CPM to such project.
Activity 3.1. Feedback
In applying the CPM, you need to take the following steps in your project;
a. Define the required tasks and put them down in an ordered (sequenced) list.
b. Create a flowchart or other diagram showing each task in relation to the others.
c. Identify the critical and non-critical relationships (paths) among tasks.
d. Determine the expected completion or execution time for each task.
e. Locate or devise alternatives (backups) for the most critical paths.
3.2. Critical Chain Project Management (CCPM)
You would recall in the introductory part of this lecture where CCPM was mentioned, it
is helpful in the sense that the limitations stated above for CPM could be surmounted by
Critical Chain Project Management (CCPM). According to Project Management Body of
Knowledge (PMBOK) in (PMI, 2001) Critical chain method is a schedule network
analysis technique that modifies the project schedule to account for limited resources. It
mixes deterministic and probabilistic approaches to schedule network analysis. The
critical chain concept was coined by Eliyahu Goldratt.
CCPM takes advantage of the best practices of:
• PMBOK: Planning and control processes.
• TOC (Theory of Constraints): Remove bottleneck to resolve constraints.
26
• Lean: Eliminate waste.
• Six Sigma: Reduce Variations.
CCPM can help to overcome following phenomenon. We have;
• Parkinson’s Law: Work expands to fill the available time.
• Student Syndrome: People start to work in full fledge only when deadline is near.
• Murphy's Law: What can go wrong will go wrong.
• Bad Multi-Tasking: Bad multitasking can delay start of the successor tasks.
You should also note that CCPM is based on:
- Resource constrained situations.
- Optimum use of Buffer (amount of time added to any task to prevent slippage of
schedule)
• Project Buffers (PB): Amount of buffer time at the end of the project.
• Feeding Buffers (FB): Amount of buffer time at the end of a sequence of tasks.
• Resource Buffers (RB): It is an alert that is used to indicate that resource is
needed to perform a task. This alert can be set few days before a resource is
needed.
Summary of Session 3
In this Session, you have learned that;
1. CPM is a method for planning, scheduling, and controlling projects.
2. CPM was developed in the 1950s by DuPont, and was first used in missile-defense
construction projects. Since that time, CPM has been adapted to other fields
including hardware and software product research and development.
3. To understand CPM further, the first thing is to understand the nature of the task.
Using the standard laid by Project Management Body of Knowledge (PMBOK),
every scheduled task can be defined by the following four parameters: Early Start
(ES); Early Finish (EF); Late Start (LS); and Late Finish (LF).
4. Key Steps in Critical Path Method are; activity specification, activity sequence
establishment, network diagram, estimates for each activity; identification of the
critical path; and critical path diagram to show project progresses.
27
5. Float time is amount of time a task can sleep before it delays project schedule.
There are two common types of floats which are free float and total float.
6. Challenges faced by CPM can be tacked with CCPM.
Self-Assessment Questions (SAQs) for Session 3
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 3.1. (tests learning outcome 3.1.)
In the statements provided below, fill in the blanks with the matching keywords.
i. CPM is a method for ______, _______ and _______projects.
ii. _________ is amount of time a task can sleep before it delays project schedule.
SAQ 3.2. (tests learning outcome 3.2.)
You have learnt in this lecture that CPM is a method for planning, scheduling, and
controlling projects. You can shed more light on this to show how relevant is it to any
significant project.
SAQ 3.3. (tests learning outcome 3.3.)
In adopting CPM for a project, what are the key steps you will take into consideration?
SAQ 3.4. (tests learning outcome 3.4.)
After taking the steps needed in SAQ 3.3., outline 3 things you think you would benefit
from using CPM and 3 things that might likely pose a challenge in its usage.
SAQ 3.5. (tests learning outcome 3.5.)
Based on what you have learnt in this lecture, identify the relevance of Critical Chain
Project Management (CCPM) to Critical Path Method (CPM).
28
References
Malakooti, B. 2013. Operations and Production Systems with Multiple Objectives. John
Wiley & Sons. ISBN 978-1-118-58537-5.
Project Management Institute 2013. A Guide to The Project Management Body Of
Knowledge (5th ed.). Project Management Institute. ISBN 978-1-935589-67-9.
Woolf, Murray B. 2012. CPM Mechanics: The Critical Path Method of Modeling Project
Execution Strategy. ICS-Publications. ISBN 978-0-9854091-0-4.
29
Study Session Four: Inventory Policy
Expected duration: 1 week or 2 contact hours
Introduction
You are welcome back from our lecture on CPM. This lecture is meant to expose you to
inventory policy. Holding stock or inventory is a very expensive issue to organisation,
particularly where the goods are of high value. However even for small value items the
cost can be high if the quantities involved are large enough. The alternative to holding
stock is to operate a Just in Time (JIT) policy where stock arrives just as it is
needed.Hence the need for you to follow along in this lecture to get the most out of it.
Learning Outcomes for Study Session 4
At the end of this lecture, it is expected that you will be able to;
4.1. Define and use correctly keywords printed in bold. (SAQ 4.1.)
4.2. Describe inventory policy with a highlight of methods best suited for an
organization. (SAQ 4.2)
4.3. Differentiate among the various types of inventory policies. (SAQ 4.3)
4.4. Identify at least 3 strategies in stock reduction. (SAQ 4.4.)
4.5. Determine order and storage costs for different order quantities with the
Economic Order Quality.
Key words; inventory, inventory policy, lead time, safety stocks, and stocks
4.1. Meaning, Methods, and Types of Inventory Policies
4.1.1. Meaning of Inventory Policy
Inventory is the physical stock of items held in any business for future productionor
sales. In a production shop the inventory may be in the form of raw materials. When the
itemsare in production process, we have the inventory as in-process inventory and at the
end of theproduction cycle inventory is in the form of finished goods. We shall be dealing
only with thefinished goods inventory.
30
There are very many inventory control policies which this lecture will look at. The most
important one is the Economic Order Quantity, or EOQ model. This is a model for
situations where there is little uncertainty in demand or delivery times. However, we will
also briefly consider a situation where there is some uncertainty in demand.
An inventory policy is a standard set of rules/boundaries and guidelines that provide the
framework for an organisation to make better informed and timely decisions on which
stock to purchase or manufacture, how much stock to purchase or manufacture and where
to store and distribute to customers. In the absence of any product knowledge or planning
parameters such as lead time, safety stocks, etc. A stockpolicy must be applied and
monitored regularly against future demand. By measuring the variability between
forecast demand and historical sales data by month, businesses will then be able to
implement the right planning parameter settings and improve their level investment in
stock.
Several stocking policies can be implemented to improve stock management
performance, these being: Reorder point; Min/Max; lot for lot; days of supply and item
location. The following components are essential for an effective inventory policy:
a. ABC Classification
b. Safety stock levels
c. The level of inventory at stocking points or locations
d. Number of warehouses or nodes
e. Number of stocking points or nodes
f. Order quantity and order frequency
g. Replenishment quantity and replenishment frequency
h. Lead time from suppliers
i. Stock obsolescence
j. Slow moving stock
k. Inventory Procedures
31
4.1.2. Inventory Methods best for Organisation
At this point, let us consider some of the inventory methods that are well suited for an
organization. We have;
1. Reorder Point - Fixed Replenishment point or fixed replenishment quantity is
used when the stock falls below a certain point which then triggers an order
release.
2. Min/Max is used when stock falls to or below the minimum stock levels which
triggers a replenishment or reorder quantity equal to the maximum level. Carton
rounding can apply with the reorder quantity to make the warehouse operation
more efficient with handling.
3. Lot for Lot or demand flow generates a new replenishment order for the same
quantity at the time the previous order arrives to your facility or operation.
4. Days of Supply (Historical demand based) is like the min / max above, however
this method relies on average daily sales using historical demand to calculate an
order quantity for a number of days’ supply.
5. Days of Supply (Forecast demand based) is like min / max above, however this
method relies on average daily sales using forecast demand to calculate an order
quantity for a number of days’ supply.
6. Item location which is based on the multi echelon optimisation approach that
incorporates greater emphasis on all elements of the entire end to end supply chain
where there is variability in demand, projections or service.
In-text Question
• During this lecture, you learnt that several stocking policies can be implemented to
improve stock management performance. In an educational organization, when
stock falls to or below the minimum stock levels which triggers a replenishment or
reorder quantity equal to the maximum level. What inventory method is this?
o Min/Max.
4.1.3. Types of Inventory Policies
1. Demand Flow: In Demand Flow policy, there is no strict inventory control.
Instead, every order that arrives at this site for this product will generate a request
for a replenishment order for the exact same quantity. All requests are driven by the
actual demand quantities received at this site for this product. Therefore, the
32
Reorder Point and Reorder/Order Up to Quantity fields are not used in this policy.
However, there is need to establish an initial inventory level. By establishing an
initial inventory level, the site will always replenish exactly what was consumed by
actual demand, whether it was filled immediately, or left unfilled as a back order.
Though it seems straightforward, Demand Flow can exhibit complex behaviour,
especially when combined with Review Period. Defining a Review Period can
produce batching. Batching occurs when the replenishment orders accumulate
during the Review Period ends and are then filled.
2. Days of Supply, Demand-Based Days of Supply (DOS): Demand is similar to an
s,S inventory policy except that the parameters for minimum and maximum levels
are specified in number of days rather than product quantities. This policy
computes the daily average of product by looking back at the actual demand. How
far back to look is given by the DOS window field.
3. Days of Supply, Forecast-Based DOS: - Forecast is similar to an s,S inventory
policy except that the parameters for minimum and maximum levels are specified
in number of days rather than product quantities. This policy computes the daily
average of product by looking forward and using forecasted demand. How far
forward to look is given by the DOS window field. Forecast quantities must be
entered in the forecast table. In short, DOS-Demand establishes inventory based on
what has happened; DOS-Forecast establishes inventory based on what you expect
to happen.
4. R, Q Targets: The” R, Q Targets” inventory policy allows the user to change the
Reorder Point (R) and Reorder Quantity (Q) based on a period designated by the
user (year, quarter, month, day, etc.)When using the R, Q Targets inventory policy,
the quantities and period are specified in the Forecasts input table. In other words,
R, Q is a fixed replenishment point/fixed replenishment quantity inventory policy.
When the inventory level on-hand falls below a certain replenishment point, R, the
site will generate a replenishment order for a certain quantity, Q, of this product.
When using this policy, the Reorder Point field is set as the trigger level. The
Reorder/Order Up to Quantity field will be the exact number of units reordered.
5. s,S Targets: The regular s,S policy is a minimum/maximum inventory policy that
says that when the inventory on-hand falls below a certain minimum s, the site will
33
request for a replenishment order that will restore the on-hand inventory to a
maximum number, S. When using this policy, the Reorder Point field is the
minimum, or trigger level. The Reorder/Order Up to Quantity field is the maximum,
or the number to which the inventory level is restored.”s,S Targets” inventory policy
is just like the regular s,S policy except that you can specify Reorder Point (s) and
Order up to Quantity (S) for certain periods. You can define the period as days,
weeks, months, years, quarters etc. When using the s,S Targets inventory policy, the
quantities and period are specified in the Forecasts input table.The main difference
between s,S and R,Q is that the s,S takes into account exactly how far below the
reorder level the inventory is when the request for replenishment is generated. The
behaviour of the system depends on how often inventory is checked. So, it is
important to select the appropriate Review Period.
In-text Question
• Inventory Policies are important as they provide organisations and businesses with
the needed guideline to manage their inventory. Can you identify and match where
each inventory policy goes in the table below (Note that the table is mixed up you
have to match a policy to where it fits rightly. The first one has been done for you)
Description Inventory policy
In this policy, every order that arrives at this site for this product
will generate a request for a replenishment order for the exact
same quantity.
Forecast-Based DOS
This policy computes the daily average of product by looking
back at the actual demand.
s,S Targets
This policy computes the daily average of product by looking
forward and using forecasted demand.
Demand-Based Days of
Supply
This inventory policy allows the user to change the Reorder Point
(R) and Reorder Quantity (Q) based on a period designated by
the user (year, quarter, month, day, etc.)
Demand order
This policy that says that when the inventory on-hand falls below
a certain minimum s, the site will request for a replenishment
order that will restore the on-hand inventory to a maximum
number, S.
R, Q Targets
(Remember your task is to match the right inventory policy to it’s correct description the first one has
been done for you)
34
4.2. Meaning of Stock and Types
A stockis a type of security that signifies ownership in a corporation and represents a
claim on part of the corporation's assets and earnings. The Physical stock an organisation
may store as an asset is in the following forms:
i. Raw Materials
ii. Work in Process
iii. Finished Goods
iv. Maintenance, Repair and Operating (MRO)
As we proceed in this lecture, you also need to learn about stock reduction.
4.2.1. Stock Reduction
Organisations must strive towards reducing stock levels on a regular basis and can adopt
several strategies to achieve the expected objective. These strategies are;
1. Direct deliveries of purchase products in raw material or assembly form can be
delivered to a manufacturing line or processing point and avoid double handling
through a warehouse process.
2. Just in time production by only making what is required resulting in lower WIP
inventory.
3. Direct Deliveries of finished goods by shipping direct from your source of supply
and avoiding your logistics network, if possible.
Box 4.1. Inventory Methods best for Organisations
The inventory methods best for organisations are;
1. Reorder point
2. Min/Max
3. Lot for lot
4. Days of supply
5. Item location
4.2.2. Why the need for Stock?
There are several core reasons why organisations need to keep a level of stock across
their operations. However, the challenge is to understand the total cost of your supply
35
chain and the impact stock can have to a range of functions and facilities for operation
within organisation. Depending upon the nature of your business or the strategy your
organisation is adopting to meet the needs of the market, understanding the total supply
chain cost will enable you to make better decisions on expanding your organisation or
scaling down the number of sites or warehouses and still achieve the right customer
service level at the right cost for your business.
At this point, let us consider some reasons for keeping stock:
i. Improve customer service
ii. Economies of scale for purchasing
iii. Transportation costs
iv. Variation in consumer demand
v. Economic conditions, strikes etc.
There are many costs associated with holding (or not holding) stock. Some of these are:
i. warehouse costs
ii. money tied up in stock (interest charges)
iii. damage while in storage
iv. deterioration while in storage
v. obsolescence
vi. ordering costs
vii. delivery costs
viii. cost of any ‘stock-outs’.
Warehouse costs include things like rental charges, heating and wages. Money that is tied
up in stock could be earning money (or reducing overdraft charges). A certain proportion
of goods will be damaged while in the warehouse or may be stolen and certain products
deteriorate (for example, food), while other items may become obsolete if stored too long
(last year’s computer will be worth less than the latest version). In addition to the costs
directly associated with the holding of stock, there is also the cost of ordering and
delivery. One of the models used when dealing with stock is the EOQ Model and it will
be discussed shortly.
36
4.3. Economic Order Quantity (EOQ) model
This is one off the models used when dealing with stock. The assumptions that must be
made before this model can be used are as follows:
i. Demand is known and constant
ii. Lead time is constant
iii. Only one item is involved
iv. Stock is monitored on a continuous basis and an order is made when the stock
v. level reaches a re-order point
vi. When an order arrives, the stock level is replenished instantaneously
vii. Stock-outs do not occur.
Fig 4.1. Economic Order Quantity Model
The Figure 4.1 above may help you picture the general problem. An order quantity Q
arrives and is used up at a constant rate, until the stock level reaches zero, at which point
a new order arrives. For small values of Q more frequent ordering will be necessary and
hence order costs will be high, while large values of Q will increase the quantity in store
and therefore increase the storage costs. The problem is to determine the value of Q that
minimizes the sum of the order costs and storage costs.
If the cost of placing an order is represented by the letter C, then the total order cost is
simply the number of orders multiplied by C. If D is the demand over a specified period,
then the number of orders must be:
Stock Level
Q2
Q Demand Steady
Instantaneously
Replenish
Average Stock Level
New order Arrives Time
37
��
and the order cost is:
� ∗��
To calculate the storage cost it is assumed that the cost of holding one unit in stock for a
specified period is known. This cost is represented by h. As the amount in stock varies we
need to calculate the average stock level, and from Figure 4.1 you can see that this must
be:
�2
Hence the storage cost is:
ℎ ∗�2
Example 1
Imagine that you work for a Computer Center of an Educational institution and you have
been asked to decide on the best inventory control policy for the computer sets. You are
told that the demand is fairly constant at 5000 units p.a. and it costs N14.40 to place an
order. You are also told that the storage cost of holding one unit of the set per annum is
N10. To investigate how inventory costs vary with order size, you decide to work out the
order and storage costs for different order quantities.
38
Solution:
This means that the two costs are equal at the optimum. This is generally true, so:
� ∗ �
= ℎ ∗ �
Multiplying both sides by 2Q and rearranging gives you:
Q2 = 2� ∗ ��
That is: (2��/ℎ)
This formula is known as the economic order quantity (EOQ), and in words it means:
(2 ∗ ���� ��� ����� ∗ ������/ℎ������ ���� ��� ���)
All you should do to use this formula is simply to substitute the values for C, D, and h.
C = Cost per Order
D = Demand
h = holding cost per unit
Use the EOQ formula to calculate the value of Q that minimizes the sum of the ordering and holding
costs. What is this cost?
For an order size of 20:
Order cost = � ∗ �
= 14.4 ∗ $%%%�%
= N3600 p.a
Storage = h ∗ �
= 10 ∗ �%�
= N100 p.a
Total cost = N3600 + N100
= N3700 p.a
39
Solution:
Time between orders and the re-order level in the Computer center showed that the
number of orders per year at the EOQ of 120 is
= $%%%&�%
= 41.67
If the institution works for 300 days a year, this means that the time between orders should be
'%%(&.)*
= 7.2 days on average
From Figure 4.1 you will see that a new order arrives just as the stock level reaches zero.
For this to happen, an order must have been placed sometime previously. In practice an
order is placed when the stock reaches a predetermined level. To calculate this level all
that is required is the lead (or delivery) time. If the lead time is, say, 4 days, then during
this time a certain amount of stock will have been sold. With a demand of 5000 a year,
the daily sales will be;
5000 = 16.7 on average
300
Q = 2 ∗ 14.4 ∗ 5000/10)
Q = √14400
Q = 2 ∗ 14.4 ∗ 5000/10)
Q = 120
and the cost is N1200 p. a.
40
In 4 days, 66.8 or about 67 games will be sold, and therefore an order will need to be
placed when the stock is down to this level. This re-order level is shown in Figure 4.2.
Fig 4.2. Reorder level in EOQ
Summary of Session 4
In this lecture, you have learned that;
1. Inventory is the physical stock of items held in any business for future
productionor sales. In a production shop the inventory may be in the form of raw
materials.
2. An inventory policy is a standard set of rules/boundaries and guidelines that
provide the framework for an organisation to make better informed and timely
decisions on which stock to purchase or manufacture, how much stock to purchase
or manufacture and where to store and distribute to customers.
3. Several stocking policies can be implemented to improve stock management
performance, these being: Reorder point; Min/Max; lot for lot; days of supply and
item location.
4. The physical stock an organisation may store as an asset is in the following forms:
raw materials; work in process; finished goods; maintenance, repair and Operating
(MRO).
5. Some reasons for keeping stock are; improve customer service; economies of scale
for purchasing; transportation costs; variation in consumer demand and economic
conditions, strikes etc.
(Lead time)
Reorder Level
Stock Level
Q
67
4 4
(Average time)
Days
7.2
41
6. The Economic Order Quantity (EOQ) model minimizes the stock holding cost
plus the ordering cost. If discounts are given for large orders, this can be cheaper
than ordering the EOQ. Most inventory systems have a buffer stock to avoid
running out of stock.
7. Economic Order Quantity (EOQ) modelassumptions are as follows; demand is
known and constant; lead time is constant; only one item is involved; stock is
monitored on a continuous basis and an order is made when the stock; level
reaches a re-order point; when an order arrives; the stock level is replenished
instantaneously and stock-outs do not occur.
Self-Assessment Questions (SAQs) for Session 4
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 4.1. (tests learning outcome 4.1.)
Identify the TRUE/FALSE statements in the list provided below.
a. Inventory is the physical stock of items held in any business for current
productionor sales.
b. An inventory policy is a standard set of rules/boundaries and guidelines that
provide the framework for an organisation to make better informed and timely
decisions on which stock to purchase or manufacture, how much stock to
purchase or manufacture and where to store and distribute to customers.
c. A stockis a type of security that signifies ownership in a corporation and
represents a claim on part of the corporation's assets and earnings.
SAQ 4.2. (tests learning outcome 4.2.)
Based on your understanding of this lecture, how would you describe inventory policies
and the methods best suited for an organization?
SAQ 4.3. (tests learning outcome 4.3.)
What major differences do you think exist between Days of Supply, Demand-Based Days
of Supply (DOS) and Days of Supply, Forecast-Based DOS.
42
SAQ 4.4. (tests learning outcome 4.4.)
You learnt in this lecture that organisations must strive towards reducing stock on regular
basis, what are some of the strategies that can be deployed in doing this?
References
Andrew C. and John L., 2010 "Economic Theory and the World of Practice: A
Celebration of the (S,s) Model", Journal of Economic Perspectives, Winter, V 24,
N 1
Malakooti, B. 2013. Operations and Production Systems with Multiple Objectives. John
Wiley & Sons. ISBN 978-1-118-58537-5
43
Study Session Five: Equipment Replacement Policies
(Individual and Mass/Group Techniques for
Non-Durable Items, Npv and Least Cost
Methods for Durable Items)
Expected duration: 2 weeks or 2 contact hours
Introduction
Welcome back to EME 302 class. This is another phase in the course where we shall be
discussing on equipment replacement policies. It is good for you to note that if any
equipment or machine is used for a long period, due to wear and tear, the item tends to
worsen. A remedial action to bring the item or equipment to the original level is desired.
Then the need for replacement becomes necessary. This need may be caused by a loss of
efficiency in a situation leading to economic decline. By passing away of time, the parts
of an item are being worn out and the cost of maintenance and operation is bound to
increase year after year. The resale value of the item goes on diminishing with the
passage of time. The depreciation of the original equipment is a factor, which is
responsible not to favour replacement because the capital is being spread over a long time
leading to a lower average cost. Thus, there exists an economic trade-off between
increasing and decreasing cost functions. So, what do we do in this situation? we strike a
balance between the two opposing costs with the aim of obtaining a minimum cost. The
problem of replacement is to determine the appropriate time at which a remedial action
should be taken which minimizes some measure of effectiveness. Another factor namely
technical and/or economic obsolescence may force us for replacement. This and more
would form the framework of this lecture. As usual I urge you to pay utmost attention.
Learning Outcomes for Study Session 5
At the end of this lecture, it is expected that you will be able to;
5.1. Define and use correctly keywords printed in bold. (SAQ 5.1.)
5.2. Explain the term “equipment replacement policies”.(SAQ 5.1.)
44
5.3. Identify items regarded as deteriorating and non- deteriorating.(SAQ 5.2)
5.4. Discuss the Net Present Value and its usage is decision-making. (SAQ 5.3.)
Key words; replacement theory, replacement, replacement policy, replacement
models, and hurdle rate.
5.1. Replacement Theory, Maintenance, and Models in Operation Research
5.1.1. Replacement Theory inOperation Research
Machine replacement problem can be linked to operation research and management
science (Nahmias, 1997). It could be regarded as Renewal theory which is a useful tool in
modeling many systems. The quantity-based replacement policy and time-based
replacement policy for a single machine problem are reported. These two kinds of
policies have been applied to inventory management problems. In a quantity-based
replacement policy, a machine is replaced when an accumulated product of size q is
produced. In this model, one must determine the optimal production size q. While in a
time-based replacement policy, a machine is replaced in every period of T. For this
model, one must determine the optimal replacement period T in each production cycle.
Replacement theory is generally concerned with theproblem of replacement of
machines, bulbs and men due to deteriorating efficiency, failure or break down.
Replacement is usually carried out under the following situations:
• When existing items have outlived their effective lives and it may not be
economical to continue with them anymore.
• When the items might have been destroyed either by accidents or otherwise.
Take note that the above replacement situations may be categorized into the following
four categories. These categories are;
• Replacement of items that deteriorated with time.
• Replacement of items which did not deteriorate but failed completely after certain
use.
• Replacement of an equipment that became out of date due to new development.
• Gradual diminishing of the existing working staff in an organization due to
retirement, death etc.
45
The Replacement Theory in Operations Research is used in the decision-making process
of replacing a used equipment with a substitute; mostly a new equipment of better usage.
The replacement might be necessary due to the deteriorating property or failure or
breakdown of equipment.
The ‘Replacement Theory’ is used in the cases like; existing items have out-lived, or it
may not be economical anymore to continue with them, or the items might have been
destroyed either by accident or otherwise. The above discussed situations can be solved
mathematically and categorised on some basis which may be called as Replacement
Models. Items that deteriorate with time e.g. machine tools, vehicles, equipment
buildings etc.
A replacement policy is a specification of “keep” or “replace” actions, one for each
period. Two simple examples are the policy of replacing the equipment every period and
the policy of keeping the first machine until the end of the period N. An optimal policy is
a policy that achieves the smallest total net cost of ownership over the entire planning
horizon and it has the property that whatever the initial state and initial decision are, the
remaining decisions must constitute an optimal policy with regard the state resulting from
the first decision. In practice, the replacement problem can be easily addressed using
dynamic programming and Markov decision processes.
In-text Question
• Dele works in the audit department of a school. He notices that the chairs in the
staff room have begun to squeak and one of the teachers had a minor accident in
the school as the legs of the chair she sat on gave way during a general staff
meeting. He immediately called for the inventory list to notice that the chairs used
in the staff room were purchased 7years ago. His immediate request school
management to change these set of furniture was instantly granted. What category
of replacement will this fall into?
o For the answer, see the note on replacement categories above.
46
Box 5.1. Replacement Theory
Replacement is usually carried out under the following situations:
1. When existing items have outlived their effective lives and it may not be economical to continue with
them anymore.
2. When the items might have been destroyed either by accidents or otherwise.
5.1.2. Replacement and Maintenance
Replacement problems involve items that degenerate with use or with the passage of time
and those that fail after a certain amount of use or time. Items that deteriorate are likely to
be large and costly (e.g., machine tools, trucks, ships, and home appliances). Non-
deteriorating items tend to be small and relatively inexpensive (e.g., light bulbs, vacuum
tubes, ink cartridges). The longer a deteriorating item is operated the more maintenance it
requires to maintain efficiency. Furthermore, the longer such an item is kept the less is its
resale value and the more likely it is to be made obsolete by new equipment. If the item is
replaced frequently, however, investment costs increase. Thus, the problem is to
determine when to replace such items and how much maintenance (particularly
preventive) to perform so that the sum of the operating, maintenance, and investment
costs is minimized.
In the case of non-deteriorating items the problem involves determining whether to
replace them as a group or to replace individuals as they fail. Though group replacement
is wasteful, labour cost of replacements is greater when done singly; for example, the
light bulbs in a large subway system may be replaced in groups to save labour.
Replacement problems that involve minimizing the costs of items, failures, and the
replacement labour are solvable either by numerical analysis or simulation.The “items”
involved in replacement problems may be people. If so, maintenance can be interpreted
as training or improvements in salary, status, or fringe benefits. Failure can be interpreted
as departure, and investment as recruiting, hiring, and initial training costs. There are
many additional complexities in such cases; for example, the effect of one person’s
resigning or being promoted on the behaviour of others. Such controllable aspects of the
environment as location of work and working hours can have a considerable effect on
productivity and failure rates. In problems of this type, the inputs of the behavioral
sciences are particularly useful.
47
In- text Question
• How do you think replacement problems that involve minimizing the cost of items, failures, and
the replacement labour can be solved?
• That is best done by numerical analysis or simulation.
5.1.3. Reasons for Equipment Replacement
The factors necessitating the replacement of machines and equipment can broadly be
classified into the following two categories:
1. Technical factors.
2. Cost factors
Box 5.2. Replacement and maintenance
Items that deteriorate are likely to be large and costly (e.g., machine tools, trucks, ships,
and home appliances). Non-deteriorating items tend to be small and relatively
inexpensive (e.g., light bulbs, vacuum tubes, ink cartridges). The longer a deteriorating
item is operated the more maintenance it requires to maintain efficiency.
The Technical factorsresponsible for equipment replacement as discussed earlier are;
1. Wear and tear of equipment
2. Obsolescence caused by new invention.
3. Unsuitability of existing equipment due to:
a. Size of the work
b. Speed of operation
c. Degree of accuracy
d. Rate of output
e. Need for power
4. Automation combining two or more processes.
5. To eliminate the slack time of some machines through line balancing.
6. Reduced safety as compared to new equipment.
7. Additional operations by the new machine.
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8. Reduction or elimination of manual operation and the resultant hazards by the new
machine.
9. Easy, quick and convenient setting-up and operation of new machine.
10. Reliability of performance
On the other hand, we also have Cost Factors such as;
1. High repair cost of existing machine
2. Reduction in the spoiled work by the new machine.
3. More output at faster rate from new machine.
4. Combination of two or more existing operations into one by a new machine.
5. Reduction in the labor cost caused by the reduced number and lower type of
operators.
6. Consumption of less power of fuel by the new machine.
7. Lesser space required by the new machine.
8. Improvement in the quality with the use of new machine.
9. Flexibility in the use of the new machine for other types of operations.
10. Probable economic life of the new machine.
11. Reduction in the cost of jigs, tools, fixtures, etc.using new machine.
12. Size of the investment required in new machine.
It should be noted that there are certain intangible factors which are incidental to
equipment replacement. They are;
1. Displacement of employees caused by replacements and
2. Introduction of hazards by new equipment.
Being intangible factors they are not measured in monetary value and hence are not
included in the replacement analysis. They involve sociological and humanitarian
considerations with far reaching influences. A careful consideration based on the above
factors must be made before implementing equipment replacement. It is prudent to defer
replacement if the information is on cards that advanced model of the same machine is
developed and is available in the very near future. This enables the replacement by state
of the art version of the machine and the replacement is more justified for the capital
invested.
49
5.1.4. Models in Replacement and Maintenance
As we proceed in this lecture, let us consider the models used in replacement and
maintenance. These are;
Model 1: “Replacement of items whose maintenance Cost increases with time and the
value of the money remains constant during the period”
Model 2: “Replacement of items whose maintenance cost increases with time and value
of money also changes with time”.
Model 3: “Group Replacement policy”
From model 1: Notation and symbols
C - Purchase cost of the machinery or equipment
S - Salvage value or resale value or scrap value of the machinery or equipment
Tc - total cost increased on the item or equipment during the period y
Then,
Tc = C + m(Y) – S
Where M(Y) is the cumulative maintenance cost in that period.
G(Y) Average cost incurred on the equipment or item during the period.
G(Y) = Tc / y
Example 5.1
The cost of the machine is N6100 and its scrap value is Rs 100 at the end of every year. The Maintenance
Cost found from experience are as follows:
Year 1 2 3 4 5 6 7 8
M.C 100 250 400 600 900 1200 1600 2000
When should the machine be replaced?
Table 5.1: Example 5.1
50
Solution to Example 5.1:
Given: C = 6100 and S = 100
Year (Y) Maintenance Cumulative
Maintenance cost
m(y)
Total Cost
C-S + m(y)
Average Cost
g(y)
1 100 100 6100 6100
2 250 350 6350 3175
3 400 750 6750 2250
4 600 1350 7350 1837.5
5 900 2250 8250 1650
6 1200 3450 9450 1575
7 1600 5050 11050 1578.5
8 2000 7050 13050 1631.25
Table 5.2: Solution to Example 5.1
It is clear from table 5.2 analysis that the machine needs to be replaced at the end of 6th
year or at the beginning of 7th year because the maintenance cost of 7th year is more than
the average cost of the machine i.e. 1578.5 > 1575.5.
5.2. Net Present Value (Npv) and Least Cost Methods
5.2.1. Net Present Value
The NPV is the value obtained by discounting all cash outflows and inflows of an
investment opportunity by a chosen rate of return. The NVP valuation method requires
estimating the size and timing of all the incremental cash flows from the project. These
future cash flows are then discounted to determine their present value. If we treat
outflows of the projects as negative and inflows as positive, the NPV of the project is the
sum of the PVs of all flows that arise because of doing the project. The NPV decision
rule is to accept all positive NPV projects in an unconstrained environment, or if projects
are mutually exclusive, accept the one with the highest NPV. If NPV is negative, the
project is not financially viable. If the NPV is zero, the project just breaks even.
The NPV is greatly affected by the discount rate, so, selecting the proper rate (sometimes
called the hurdle rate) is critical to making the right decision. The hurdle rate is the
minimum acceptable return on an investment. It should reflect the riskiness of the
investment, typically measured by the volatility of cash flows, and must consider the
51
financing mix. Managers may use models such as the CAPM or the APT to estimate a
discount rate appropriate for each particular project, and use the weighted average cost of
capital (WACC) to reflect the financing mix selected. A common practice in choosing a
discount rate for a project is to apply a WACC that applies to the entire firm, but a higher
discount rate may be more appropriate when a project's risk is higher than the risk of the
firm.
5.2.2. Advantages of Net Present Value (NPV)
At this point, let us consider some of the advantages of Net Present Value. These are;
1. It considers the time value of money.
2. It is an absolute measure of return.
3. It uses cash flows and not profits.
4. It considers the whole life of the project.
5. It leads to selection of project that increase shareholders’ wealth.
5.2.3. Disadvantages of NPV
Here are some of the disadvantages of NPV. We have;
1. It is difficult to explain to managers
2. It requires knowledge of the cost of capital
3. It is relatively difficult to calculate (compare to ARR and Payback period)
In-text Question
• The NVP valuation method requires estimating the size and timing of all the
decremental cash flows from the project. Do you support this statement?
• No, NPV only monitors incremental cash flows from the project.
Example 5.2
Shaw Limited is considering a capital investment costing 180,000. The estimated cash
flows are given as follows:
Year Cash flow
1 90,000
2 110,000
3 60,000
4 40,000
Table 5.3: Example 5.2
52
The company’s cost of capital is 15%. What is the NPV of the project, and should it be
undertaken?
Solution to example 5.2
Year Cash flow Discounting factor @
15%
Present Value
0 (180,000) 1.000 (180,000)
1 90,000 0.870 78,300
2 110,000 0.756 83,160
3 60,000 0.658 39,480
4 40,000 0.572 22,880
Net Present Value 43,820
Table 5.4: Solution to Example 5.2
Since the NPV is positive, the project should be undertaken.
5.2.4.Least Cost Method
In least cost method, you should start by giving allocations from the minimum cost in the
matrix. It means that cell for which cost is minimum is given allocation first. Then
allocation is given in next minimum cost and so on. It means lower cost cells are given
priority over higher cost cells.Other steps are;
STEP 1: Determine the least cost among all the rows of the transportation table.
STEP 2: Identify the row and allocate the maximum feasible quantity in the cell
corresponding to the least cost in the row. Then eliminate that row (column)
when an allocation is made.
STEP 3: Repeat steps 1 and 2 for the reduced transportation table until all the
available quantities aredistributed to the required places. If the minimum cost
is not unique, the tie can be broken arbitrarily.
To illustrate, consider this example;
53
Example 5.3
Origin P Q R Supply
A 5 7 8 70
B 4 4 6 30 0
C 6 7 7 50
Demand 65 42 43
55
Table 5.5: Destination
We examine the rows A, B and C, 4 is the least
cost element in the cell (B,P) and (B, Q) and the
tie can be broken arbitrarily. Select (B, P).The
origin B can supply 30 items to P and thus origin
B is exhausted. P still requires 35 more units.
Hence, deleting the row B, we have the reduced
matrix as in the table 5.6.
Origin P Q R Supply
A 35
5
7
8
70
35
C 6 7 7 50
Demand 35 42 43
0
Table 5.6: Destination
In the reduced matrix (table 5.6) we observe that
5 is the least element in the cell (A, P) and
examine the supply at A and demand at P. The
destination P requires 35 items and this
requirement is satisfied from A so that the
column P is deleted next. So, we have the reduce
matrix as in table 5.7.
Origin Q R Supply
A 35
7
8
35
0
C 7 7 50
Demand 35 43
7
Table 5.7: Destination
In the reduced matrix (table 5.7) we choose 7 as
least element corresponding to the cell (A. Q).
Wesupply 35 units from A to Q so have the
reduced matrix in table 5.8.
Origin Q R Supply
A 7
7
43
8
50
0
Demand 7 43
0 0
Table 5.8: Destination
Now, only one row is left behind. Hence, we
allow 7 items from C to Q and 43 items C to R.
We now have the allotment as per the least cost
method as shown in the table 5.9
Origin P Q R Supply
A 35 35 70
B 30 30
C 7 43 50
Demand 65 42 43
Table 5.8: Destination
The cost of the allocation by the least cost
method is 35 × 5 + 35 × 7 + 30 × 4 + 7 × 7 + 43
× 7 = N890
54
Summary of Session 5
In this lecture, you have learned that;
1. Replacement theory is generally concerned with theproblem of replacement of
machines, bulbs and men due to deteriorating efficiency, failure or break down.
2. Replacement is usually carried when existing items have outlived their effective
lives and it may not be economical to continue with them anymore or after been
destroyed by accidents or otherwise.
3. The Replacement Theory in Operations Research is used in the decision-making
process of replacing a used equipment with a substitute; mostly a new equipment
of better usage.
4. A replacement policy is a specification of “keep” or “replace” actions, one for
each period. Two simple examples are the policy of replacing the equipment every
period and the policy of keeping the first machine until the end of the period N.
5. Replacement problems involve items that degenerate with use or with the passage
of time and those that fail after a certain amount of use or time.
6. The factors necessitating the replacement of machines and equipment can broadly
be classified into the following two categories: technical and factors.
7. The models in replacement and maintenance are; replacement of items whose
maintenance cost increases with time and the value of the money remains constant
during the period; replacement of items whose maintenance cost increases with
time and value of money also changes with time; and Group Replacement policy.
8. The Net Present Value (NPV) is the value obtained by discounting all cash
outflows and inflows of an investment opportunity by a chosen rate of return. The
NPV decision rule is to accept all positive NPV projects in an unconstrained
environment, or if projects are mutually exclusive, accept the one with the highest
NPV.
9. In least cost method, you should start by giving allocations from the minimum cost
in the matrix. It means that cell for which cost is minimum is given allocation first.
Self-Assessment Questions (SAQs) for Session 5
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
55
SAQ 5.1. (tests learning outcomes 5.1. and 5.2.)
Using the statements provided below, identify the TRUE/FALSE items.
a. Replacement theory is generally concerned with theproblem of replacement of
machines, bulbs and men due to deteriorating efficiency, failure or break down.
b. Replacement happens when existing items have s newer version or models.
c. A replacement policy is a specification of “keep” or “replace” actions, one for
each period.
d. Replacement Models is used solved qualitatively and categorised on some basis
which may be called as.
e. The hurdle rate is the minimum acceptable return on an investment.
SAQ 5.2. (tests learning outcome 5.3.)
Replacement problems involve items that degenerate with use or with the passage of time
and those that fail after a certain amount of use or time. Kindly distinguish between these
items.
SAQ 5.3. (tests learning outcome 5.4)
As an expert in management, how would you describe net present value and its relevance
to managerial decisions?
References
Hira D.S., 2004 Operation Research, S.Chand & Company Ltd., New Delhi.
Nahmias, S. 1997. Production and Operation Analysis, McGraw Hill International,
Chicago.
Taha, H. A, 2013 Operation Research - An Introduction, Prentice Hall of India, 7th
edition, Ravindran, Phillips and Solberg, Operations Research: Principles and
Practice, John Wiely & Sons, 2nd Edition.
56
Study Session Six: Queuing Theory
Expected duration: 1 week or 2 contact hours
Introduction
I hope you have been finding this course educative? This another phase in EME 302
where the focus will be on Queuing Theory. It is a common phenomenon in everyday life
to see many people waiting in front of abooking counter in a railway station or in a
theatre or in a ration shop to have some service carried out. This formation of queue
occurs whenever the present demand for a service exceeds the present capacity to provide
the necessary government, industry, schools, hospitals, etc.Thus, this lecture has been
geared towards equipping you with the necessary skills needed to manage such.
Learning Outcomes for StudySession 6
At the end of this lecture, it is expected that you will be able to;
6.1. Define and use correctly keywords printed in bold. (SAQ 6.1.)
6.2. Explain Queuing Theory.(SAQ 6.2)
6.3. Identify terms used in queuing model. (SAQ 6.1)
6.4. Describe how an effective Queuing system can be designed. (SAQ 6.3)
6.5. Clearly differentiate between the various Queuing notations. (SAQ 6.1)
Key word; queuing theory.
6.1. Meaning and Definition of Terms in Queuing Theory
6.1.1. Meaning of Queuing Theory
To kick-start this lecture, let us take a moment to discuss on man’s daily activities. From
the time of birth (usually involving an approximately 9-month period from the moment of
conception) until death (an entire life-time - whether brief, extensive or in between) and
at many moments along the way human beings often find themselves waiting for things,
events, conditions, etc. A major topic of Applied Mathematics that deals with this
phenomenon of waiting is called Queuing Theory. Using the word "Queue", which is
57
more common in British than American English and means "a line up" or "to form a
line", a closely reasoned body of mathematical theory has been developed to describe this
common human activity; theory applicable to normal economic activity. Realistic
applications can be made to the phenomena of customers awaiting the delivery of
goods/services, as well as to goods-in-process coming to be finished goods.
The first queuing theory problem was considered by Erlang in 1908 who looked at how
large a telephone exchange needed to be to keep to a reasonable value the number of
telephone calls not connected because the exchange was busy (lost calls). Within ten
years he had developed a (complex) formula to solve the problem. Queuing theory is
used to develop more efficient queuing systems that reduce customer wait times and
increase the number of customers that can be served. For example, a 2003 paper by
Stanford School of Business professor Lawrence Wein used queuing theory to analyze
the potential effects of a bioterrorism attack on U.S. soil and propose a system to reduce
wait times for medications that would decrease the number of deaths caused by such an
attack.
Queuing theory is the mathematical study that deals with problems which involve
queuing (or waiting lines), or queues. In queuing theory, a model is constructed so that
queue lengths and waiting times can be predicted. Queuing theory is generally considered
a branch of operations research because the results are often used when making
organisation decisions about the resources needed to provide a service.
6.1.2. Definition of Terms inQueuing Model
Customer: The arriving unit that requires some service to be provided is called the
customer. The customer may represent people, machines, etc.
Server: A server is one who provides the arriving customer the necessary service. It may
be personsin the counter or machines, etc.
Waiting Line or Queue: The queue represents the number of customers waiting to be
served.Normally the queue does not include the customer being served.
Service Channel: This refers to the type of service provided. If we have one serving unit
only, we have a single channel model or single server model. If service involves more
58
than one server, we have a multi-channel server model. We use the symbol k to denote
the number of service channels.
Real-life applications of queuing theory include:
a. providing faster customer service,
b. improving traffic flow,
c. shipping orders efficiently from a warehouse,
d. designing telecommunications systems such as call centers.
e. banks/supermarkets - waiting for service
f. computers - waiting for a response
g. failure situations - waiting for a failure to occur e.g. in a piece of machinery
h. public transport - waiting for a train or a bus
As we know queues are common in every-day experience as seen in Fig 6.1. Queues
form because resources are limited. In fact, it makes economic sense to have queues. For
example,imagine how many supermarket tills you would need to avoid queuing? how
many buses or trains would be needed if queues were to be avoided/eliminated?
Fig 6.1. An image showing Nigerians who queued while waiting to cast their votes in the last election
Image source: http://www.nigerianeye.com/2015/03/nigeria-decides-2015-live-update.html
59
In designing queuing systems, we need to aim for a balance between service to customers
(short queues implying many servers) and economic considerations (not too many
servers). In essence, all queuing systems can be broken down into individual sub-systems
consisting of entities queuing for some activity. Typically, we can talk of this individual
sub-system as dealing with customers queuing for service. To analyse this sub-system we
need information relating to:
Arrival process:
This answer questions such as;
� how customers arrive e.g. singly or in groups (batch or bulk arrivals)
� how the arrivals are distributed in time (e.g. what is the probability distribution of
time between successive arrivals (the inter-arrival time distribution)
� whether there is a finite population of customers or (effectively) an infinite
number
The simplest arrival process is one where we have completely regular arrivals (i.e. the
same constant time interval between successive arrivals). A Poisson stream of arrivals
corresponds to arrivals at random. In a Poisson stream successive customers arrive after
intervals which independently are exponentially distributed. The Poisson stream is
important as it is a convenient mathematical model of many real-life queuing systems and
is described by a single parameter - the average arrival rate. Other important arrival
processes are scheduled arrivals; batch arrivals; and time dependent arrival rates (i.e. the
arrival rate varies according to the time of day).
In-text Question
• You meet Bisi and James at an ATM booth collection. James laments that inspite
of the fact that there 5 functional ATMs. The queues remain overwhelming.
Explain to him the sense around this phenomenon and how this can be managed
through designing queuing systems.
• When explaining to James note that queues form because resources are limited. In
fact, it makes economic sense to have queues. For example, imagine how many
supermarket tills you would need to avoid queuing? how many buses or trains
would be needed if queues were to be avoided/eliminated?
60
• In designing queuing systems, we need to aim for a balance between service to
customers (short queues implying many servers) and economic considerations (not
too many servers).
Another information that is needed in designing queuing model is known as;
Service mechanism: This caters for information such as;
� a description of the resources needed for service to begin
� how long the service will take (the service time distribution)
� the number of servers available
� whether the servers are in series (each server has a separate queue) or in parallel
(one queue for all servers)
� whether preemption is allowed (a server can stop processing a customer to deal
with another "emergency" customer)
If the service times for customers are independent and do not depend upon the arrival
process is common. Another common assumption about service times is that they are
exponentially distributed.
As we proceed on the information needed to analyse a sub system, another needed
information is the;
Queue characteristics: this answer questions such as;
� how, from the set of customers waiting for service, do we choose the one to be
served next (e.g. FIFO (first-in first-out) - also known as FCFS (first-come first
served); LIFO (last-in first-out); randomly) (this is often called the queue
discipline)
� do we have:
o balking (customers deciding not to join the queue if it is too long)
o reneging (customers leave the queue if they have waited too long for service)
o jockeying (customers switch between queues if they think they will get served
faster by so doing)
o a queue of finite capacity or (effectively) of infinite capacity
Changing the queue discipline (the rule by which we select the next customer to be
served) can often reduce congestion. Often the queue discipline "choose the customer
with the lowest service time" results in the smallest value for the time (on average) a
61
customer spends queuing.
Note here that integral to queuing situations is the idea of uncertainty in, for example,
inter-arrival times and service times. This means that probability and statistics are needed
to analyse queuing situations. In terms of the analysis of queuing situations the types of
questions in which we are interested are typically concerned with measures of system
performance and might include the following;
Pause to consider these questions;
� How long does a customer expect to wait in the queue before they are served, and
how long will they have to wait before the service is complete?
� What is the probability of a customer having to wait longer than a given time
interval before they are served?
� What is the average length of the queue?
� What is the probability that the queue will exceed a certain length?
� What is the expected utilisation of the server and the expected time during which
he will be fully occupied (remember servers cost us money so we need to keep
them busy)? In fact, if we can assign costs to factors such as customer waiting
time and server idle time then we can investigate how to design a system at
minimum total cost.
Box 6.1. Queue Characteristics
Under queue characteristics, we have the following;
1. Balking (customers deciding not to join the queue if it is too long)
2. Reneging (customers leave the queue if they have waited too long for service)
3. Jockeying (customers switch between queues if they think they will get served faster
by so doing)
4. A queue of finite capacity or (effectively) of infinite capacity.
These are questions that need to be answered so that management can evaluate
alternatives tocontrol/improve the situation. Some of the problems that are often
investigated in practice are:
� Is it worthwhile to invest effort in reducing the service time?
� How many servers should be employed?
� Should priorities for certain types of customers be introduced?
62
� Is the waiting area for customers adequate?
To get answers to the above questions there are two basic approaches:
• analytic methods or queuing theory (formula based); and
• simulation (computer based).
The reason for being two approaches (instead of just one) is that analytic methods are
only available for relatively simple queuing systems. Complex queuing systems are
almost always analysed using simulation (more technically known as discrete-event
simulation).
At this point, you need to note that the simple queuing systems that can be tackled via
queuing theory essentially have the following features;
• consist of just a single queue; linked systems where customers pass from one
queue to another cannot be tackled via queuing theory
• have distributions for the arrival and service processes that are well defined (e.g.
standard statistical distributions such as Poisson or Normal); systems where these
distributions are derived from observed data, or are time dependent, are difficult to
analyse via queuing theory.
Activity 6.1.
Recall some of your experiences on the queue and identify some of the people you have
queued with in relation to queue characteristics you learnt in this lecture.
Activity 6.1. Feedback
You should have met this set of people;
a. Balking (customers deciding not to join the queue if it is too long)
b. Reneging (customers leave the queue if they have waited too long for service)
c. Jockeying (customers switch between queues if they think they will get served
faster by so doing).
63
Additional queuing theory information are:
Queuing notation and a simple example
It is common to use the symbols:
λ = Arrival Rate: lamda to be the mean (or average) number of arrivals per time, i.e. the
mean arrival rate
µ = Service Rate: µ to be the mean (or average) number of customers served per time,
i.e. the mean service rate
Therefore, ρ = λ / µ
Others are:
There is a standard notation system to classify queuing systems as A/B/C/D/E, where:
� A represents the probability distribution for the arrival process
� B represents the probability distribution for the service process
� C represents the number of channels (servers)
� D represents the maximum number of customers allowed in the queuing system
(either being served or waiting for service).
� E represents the maximum number of customers in total
Common options for A and B are:
• M for a Poisson arrival distribution (exponential interarrival distribution) or a
exponential service time distribution
• D for a deterministic or constant value
• G for a general distribution (but with a known mean and variance)
If D and E are not specified, then it is assumed that they are infinite.
While:
M/D/1 case (random Arrival, Deterministic service, and one service channel)
Expected average queue length E(m)= (2ρ- ρ2)/ 2 (1- ρ)
Expected average total time E(v) = 2- ρ / 2 µ (1- ρ)
Expected average waiting time E(w) = ρ / 2 µ (1- ρ)
64
Summary of Session 6
In this lecture, you have learned that;
1. A queue is a waiting line, and queuing involves dealing with items or people in
sequence. Thus, a queuing problem consists either of determining what facilities to
provide or scheduling the use of them.
2. The first queuing theory problem was considered by Erlang in 1908 who looked at
how large a telephone exchange needed to be to keep to a reasonable value the
number of telephone calls not connected because the exchange was busy (lost
calls).
3. Queuing theory is the mathematical study that deals with problems which involve
queuing (or waiting lines), or queues.
4. In designing queuing systems, we need to aim for a balance between service to
customers (short queues implying many servers) and economic considerations (not
too many servers).
5. To analyse queuing problem, there is a need to analyse the; arrival process; service
mechanism; and queue characteristics.
6. Questions that need to be answered so that management can evaluate alternatives
to control/improve the situation. Some of the problems that are often investigated
in practice are; is it worthwhile to invest effort in reducing the service time? how
many servers should be employed? should priorities for certain types of customers
be introduced? is the waiting area for customers adequate?
Self-Assessment Questions (SAQs) for Session 6
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 6.1. (tests learning outcomes 6.1, 6.3, and 6.5.)
In the statements provided below, select the appropriate option that fits each item
1. _________ is the mathematical study that deals with problems which involve
queuing (or waiting lines), or queues.
a). Queuing systems b. Queuing theory c) Queuing model d)Queuing time.
65
2. Which of these is not a term in Queuing theory?
a). Server b). Waiting Queuing c). Service channel. d) Custody.
3. Real-life applications of queuing theory include;
a). providing slow customer service b). improving traffic light. c) shipping orders
efficiently from a warehouse. d) banks/supermarkets - waiting for order.
4. Which of the following is not a term in queuing model?
a) Network server b) customer c) waiting line d) Queuing channel.
5. Which of the following queuing notation has the corresponding meaning?
a). λ = Service Rateb). µ = Arrival Rate c) G for a general distribution. d)
A represents the probability distribution for the service process.
SAQ 6.2. (tests learning outcome 6.2.)
Based on what you have learnt in this lecture, simply explain what Queueing theory
entails.
SAQ 6.3. (tests learning outcome 6.3.)
While standing on the queue to pay your departmental levy in school, you observed that
you have spent 45mins on the queue causing you to miss one of your lectures for that
day. Write a report to your Head of Department clearly stating how an effective queuing
system can be designed for your department to save time spent on the queue by students.
References
Artalejo, J., and Gómez-Corral, A. 2008; Retrial queuing systems. Springer, Berlin.
Dattatreya, G. 2008; Performance analysis of queuing and computer networks. CRC
Press, Boca Raton.
Ivo, A. and Jacques R. 2002; Queuing Theory; Department of Mathematics and
Computing Science, Eindhoven University of Technology P.O. Box 513, 5600
MB Eindhoven, The Netherlands.
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Study Session Seven: Total Quality Management in Education
Expected duration: 1 week or 2 contact hours
Introduction
This is another lecture in (EME 310) Operations Management in Educational Practice. In
this lecture, we shall be considering Total Quality Management (TQM) in Education. It is
essential to know that TQM is a timely tool which must be clearly understood, adopted
and implemented as soon as possible. This lecture discusses various concepts, issues,
processes, models and implementation strategies for TQM in educational settings. Right
from creation, the idea of management arose out of the need for survival. The needs of
people then were simple. Today our needs are complex and sometimes out of place. It has
become necessary to improve development through the vehicles of education, science and
technology, hence the need for Total Quality Management.
Learning Outcomes for Study Session 7
At the end of this lecture, it is expected that you will be able to;
7.1. Define and use correctly keywords printed in bold. (SAQ 7.1.)
7.2. Trace timeline of events in the origin of TQM. (SAQ 7.2)
7.3. Discuss the relevance of TQM in an organization. (SAQ 7.3)
7.4. Identify the 8 primary elements of TQM. (SAQ 7.4)
7.5. Outline at least 6 generic models for implementing TQM. (SAQ 7.5)
Key words: total quality management, profitability, competitiveness, implementation,
technical, operational, and process.
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7.1. Origin, Meaning, and Principles of Total Quality Management
7.1.1. The Origin of Total Quality Management
Total Quality Management (TQM)in the form of statistical quality control was invented
by Walter A. Shewhart. It was initially implemented at Western Electric Company in the
form developed by Joseph Juran who had worked there with the method. TQM was
demonstrated on a grand scale by Japanese industry through the intervention of W.
Edwards Deming with the help of missionary labors in the U.S. and across the world. He
is the "father" of quality control, quality circles, and quality movement generally. Walter
Shewhart, then working at Bell Telephone Laboratories first devised a statistical control
chart in 1923; it is still named after him. He published his method in 1931 as Economic
Control of Quality of Manufactured Product. The method was first introduced at Western
Electric Company's Hawthorn plant in 1926. Joseph Juran was one of the people trained
in the technique. In 1928, he wrote a pamphlet entitled Statistical Methods Applied to
Manufacturing Problems. This pamphlet was later incorporated into the AT&T Statistical
Quality Control Handbook, still in print. In 1951, Juran published his very influential
Quality Control Handbook.
W. Edwards Deming trained as a mathematician and statistician, went to Japan at the
behest of the U.S. State Department to help Japan in the preparation of the 1951 Japanese
Census. The Japanese were already aware of Shewhart's methods of statistical quality
control. Japanese application of the method had significant and undeniable results
manifesting as dramatic increases in Japanese product quality and Japanese success in
exports. This led to the spread of the quality movement across the world.
In the late 1970s and 1980s, U.S. producers scrambled to adopt quality and productivity
techniques that might restore their competitiveness. Deming's approach to quality control
came to be recognized in the United States, and Deming himself became a sought-after
lecturer and author. Total Quality Management, the phrase applied to quality initiatives
proffered by Deming and other management gurus became a staple of American
enterprise by the late 1980s. But while the quality movement has continued to evolve
beyond its beginnings, many of Deming's emphases, particularly those associated with
management principles and employee relations were not adopted in Deming's sense but
68
continued as changing fads, including the movement to "empower" employees and to
make "teams" central to all activities.
TQM in education surfaced in 1988 at Mt. Edgecombe High school in Sitka, Alaska,
when David Langford, the school’s technology teacher/coordinator, applied Total Quality
concepts in his classes. TQM has become increasingly popular in education, as evidenced
by the plethora of books and journal articles since 1990 (Tucker 1992). TQM has also
spread into mainstream of educational organisations. The Association for Supervision
and Curriculum Development devoted its entire November, 1992 issue of its journal;
Educational Leadership to the quality movement in education.
7.1.2. Meaning of Total Quality Management (TQM)
Total Quality Management (TQM) refers to management methods used to enhance
quality and productivity in profit making organizations. In other words, Total Quality
Management (TQM) describes a management approach to long–term success through
customer satisfaction. In a TQM effort, all members of an organization participate in
improving processes, products, services, and the culture in which they work.TQM is a
comprehensive management approach that works horizontally across an organization,
involving all departments and employees and extending backward and forward to include
both suppliers and clients/customers. TQM is only one of many acronyms used to label
management systems that focus on quality. Other acronyms include CQI (continuous
quality improvement), SQC (statistical quality control), QFD (quality function
deployment), QIDW (quality in daily work), TQC (total quality control), etc. Like many
of these other systems, TQM provides a framework for implementing effective quality
and productivity initiatives that can increase the profitability and competitiveness of
organizations.
In-text Question
• Mr Dauda’s school has been in operation for over 5years. He has there have been
several complaints from parents of poor teaching standards and general attitude of
staff towards their job. He is at loss as to the next step. In view of what you have
just learnt explain to him what TQM is and how this problem can be curbed and
eventually solved if he chooses to use TQM.
69
o Recall that TQM refers to management methods used to enhance quality and
productivity in profit making organizations. In other words, Total Quality
Management (TQM) describes a management approach to long–term success
through customer satisfaction.
Let’s continue our discussion,
In view of the framework discussed earlier, TQM is a management philosophy that seeks
to integrate all organizational functions (marketing, finance, design, engineering, and
production, customer service, etc.) to focus on meeting customer needs and
organizational objectives. TQM views an organization as a collection of processes. It
maintains that organizations must strive to continuously improve these processes by
incorporating the knowledge and experiences of workers. The simple objective of TQM
is "Do the right things, right the first time, every time". TQM is infinitely variable and
adaptable. Although originally applied to manufacturing operations, and for some years
only used in that area, TQM is now becoming recognized as a generic management tool,
just as applicable in service and public sector organizations. There are some evolutionary
strands with different sectors creating their own versions from the common ancestor.
TQM is the foundation for activities, which include:
1. Commitment by senior management and all employees
2. Meeting customer requirements
3. Reducing development cycle times
4. Just in Time/Demand Flow Manufacturing
5. Improvement teams
6. Reducing product and service costs
7. Systems to facilitate improvement
8. Line Management ownership
9. Employee involvement and empowerment
10. Recognition and celebration
11. Challenging quantified goals and benchmarking
12. Focus on processes / improvement plans
13. Specific incorporation in strategic planning
70
In respect to TQM foundational activities stated above, you will observe that this shows
that TQM must be practiced in all activities, by all personnel, in Manufacturing,
Marketing, Engineering, Research and Development (R&D), Sales, Purchasing, HR, etc.
Fig 7.1. Foundations of Total Quality Management
If you take a good look at Fig. 7.1., you will realise that the core of TQM is the customer-
supplier interfaces both externally and internally and at each interface lie a few processes.
This core must be surrounded by commitment to quality, communication of the quality
message, and recognition of the need to change the culture of the organization to create
total quality. These are the foundations of TQM and they are supported by the key
management functions of people, processes and systems in the organization as shown in
Fig 7.1.
Culture
Commitment
Communication
Systems
Processes
Customer
Supplier
People
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Box 7.1. Features of TQM
TQM is a management philosophy that seeks to integrate all organizational functions
(marketing, finance, design, engineering, and production, customer service, etc.) to focus
on meeting customer needs and organizational objectives. TQM views an organization as
a collection of processes. It maintains that organizations must strive to continuously
improve these processes by incorporating the knowledge and experiences of workers.
7.1.3. Total Quality Management (TQM)Principles
At this point, let us consider the principles of TQM. Different consultants and schools of
thought emphasize different aspects of TQM as it has developed over time. These aspects
may be technical, operational, or social/managerial.The basic elements of TQM, as
expounded by the American Society for Quality Control, are
1. policy, planning, and administration;
2. product design and design change control;
3. control of purchased material;
4. production quality control;
5. user contact and field performance;
6. corrective action; and
7. employee selection, training, and motivation.
The real root of the quality movement or the "invention" on which it rests is statistical
quality control. SQC is retained in TQM in the fourth element, above, "production quality
control." It may also be reflected in the third element, "control of purchased material,"
because SQC may be imposed on vendors by contract.In a nutshell, this core method
requires that quality standards are first set by establishing measurements for an item and
thus defining what constitutes quality. The measurements may be dimensions, chemical
composition, reflectivity, etc. in effect any measurable feature of the object. Test runs are
made to establish divergences from a base measurement (up or down) which are still
acceptable. This "band" of acceptable outcomes is then recorded on one or several
Shewhart charts. Quality control then begins during the production process itself.
Samples are continuously taken and immediately measured, the measurements recorded
on the chart(s). If measurements begin to fall outside the band or show an undesirable
72
trend (up or down), the process is stopped and production discontinued until the causes of
divergence are found and corrected. Thus, SQC, as distinct from TQM, is based on
continuous sampling and measurement against a standard and immediate corrective
action if measurements deviate from an acceptable range.
In-text Question
• Can you identify the real root of the quality movement or the "invention" on which
it rests?
o Yes, that is statistical quality control (SQC) which is retained in TQM in the
fourth element.
7.2. The Elements, Generic Model, and Building Blocks of Total Quality
Management (TQM)
7.2.1. The Primary Elements of TQM
We have come to another section of this lecture where we shall discuss the primary
elements of TQM. Total quality management can be summarized as a management
system for a customer-focused organization that involves all employees in continual
improvement. It uses strategy, data, and effective communications to integrate the quality
discipline into the culture and activities of the organization. These elements are discussed
as follows;
1. Customer-focused: The customer ultimately determines the level of quality. No
matter what an organization does to foster quality improvement—training
employees, integrating quality into the design process, upgrading computers or
software, or buying new measuring tools—the customer determines whether the
efforts were worthwhile.
2. Total employee involvement: All employees participate in working toward
common goals. Total employee commitment can only be obtained after fear has
been driven from the workplace, when empowerment has occurred, and
management has provided the proper environment. High-performance work
systems integrate continuous improvement efforts with normal business
operations. Self-managed work teams are one form of empowerment.
3. Process-centered: A fundamental part of TQM is a focus on process thinking. A
process is a series of steps that take inputs from suppliers (internal or external) and
73
transforms them into outputs that are delivered to customers (again, either internal
or external). The steps required to carry out the process as defined, and
performance measures are continuously monitored to detect unexpected variation.
4. Integrated system: Although an organization may consist of many different
functional specialties often organized into vertically structured departments, it is
the horizontal processes interconnecting these functions that are the focus of
TQM. These processes are;
• Micro-processes add up to larger processes, and all processes aggregate into
the business processes required for defining and implementing strategy.
Everyone must understand the vision, mission, and guiding principles as well
as the quality policies, objectives, and critical processes of the organization.
Business performance must be monitored and communicated continuously.
• An integrated business system may be modeled after the Baldrige National
Quality Program criteria and/or incorporate the ISO 9000 standards. Every
organization has a unique work culture, and it is virtually impossible to achieve
excellence in its products and services unless a good quality culture has been
fostered. Thus, an integrated system connects business improvement elements
to continually improve and exceed the expectations of customers, employees,
and other stakeholders.
5. Strategic and systematic approach: A critical part of the management of quality is
the strategic and systematic approach to achieving an organization’s vision,
mission, and goals. This process, called strategic planning or strategic
management, includes the formulation of a strategic plan that integrates quality as
a core component.
6. Continual improvement: A major thrust of TQM is continual process
improvement. Continual improvement drives an organization to be both analytical
and creative in finding ways to become more competitive and more effective at
meeting stakeholder expectations.
7. Fact-based decision making: To know how well an organization is performing,
data on performance measures are necessary. TQM requires that an organization
continually collect and analyze data to improve decision making accuracy, achieve
consensus, and allow prediction based on history.
74
8. Communication: During times of organizational change, as well as part of day-to-
day operation, effective communication plays a large part in maintaining morale
and in motivating employees at all levels. Communication involve strategies,
method, and timeliness.
These elements are considered so essential to TQM that many organizations define them
as a set of core values and principles on which the organization is to operate.
Box. 7.2. The Primary Elements of TQM
The elements of TQM are;
1. Customer-focused
2. Total employee involvement:
3. Process-centered:
4. Integrated system
5. Strategic and systematic approach
6. Continual improvement
7. Fact-based decision making
8. Communication
7.2.2. Generic Model for Implementing TQM
As we proceed in our lecture on TQM in Education, another point we need to consider is
the generic model for implementing TQM. Some of these are;
1. Top management learns about and decides to commit to TQM. TQM is identified
as one of the organization’s strategies.
2. The organization assesses current culture, customer satisfaction, and quality
management systems.
3. Top management identifies core values and principles to be used, and
communicates them.
4. A TQM master plan is developed based on steps 1, 2, and 3.
5. The organization identifies and prioritizes customer demands and aligns products
and services to meet those demands.
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6. Management maps the critical processes through which the organization meets its
customers’ needs.
7. Management oversees the formation of teams for process improvement efforts.
8. The momentum of the TQM effort is managed by the steering committee.
9. Managers contribute individually to the effort through planning, training,
coaching, or other methods.
10. Daily process management and standardization take place.
11. Progress is evaluated and the plan is revised as needed.
12. Constant employee awareness and feedback on status are provided and a
reward/recognition process is established.
In-text Question
• Do remember Mr Dauda the school owner, who you advised to use TQM to get his
school back into running optimally? (see in text question in section 7.1.2) He
decided to take your advise and use TQM. However, he is doesn’t know how he
can go about using TQM. So he has come to you for help. This time, your task is
to explain to him the Generic Model for Implementing TQM in his school. You
can start with the first five points.
o Refer to section 7.2.2 of this study session as you guide Mr Dauda
7.2.3. The Buildingblocks of TQM
The building blocks of TQM are: processes, people, management systems and
performance measurement.
You need to understand that everything we do is a Process, which is the transformation
of a set of inputs, which can include action, methods and operations, into the desired
outputs, which satisfy the customers’ needs and expectations. In each area or function
within an organization there will be many processes taking place, and each can be
analyzed by an examination of the inputs and outputs to determine the action necessary to
improve quality. In every organization, there are some very large processes which are
groups of smaller processes called key or core business processes. These must be carried
out well if an organization is to achieve its mission and objectives. This section on
processes discusses processes and how to improve them, and implementation covers
how to prioritize and select the right process for improvement.
76
Fig 7.2. The building blocks of TQM
Considering Fig 7.2, you will observe that the only point at which true responsibility for
performance and quality can lie is with the people who do the job or carry out the
process, each of which has one or several suppliers and customers. An efficient and
effective way to tackle process or quality improvement is through teamwork. However,
people will not engage in improvement activities without commitment and recognition
from the organization’s leaders, a climate for improvement and a strategy that is
implemented thoughtfully and effectively. The section on people expands on these issues,
covering roles within teams, team selection and development and models for successful
teamwork.
As we continue our discussion on the building blocks of TQM, you should note that an
appropriate documented Quality Management System will help an organization not only
achieve the objectives set out in its policy and strategy, but also sustain and build upon
them. It is imperative that the leaders take responsibility for the adoption and
documentation of an appropriate management system in their organization if they are
serious about the quality journey. The Systems section discusses the benefits of having
Suppliers Customers
Outputs Inputs
Materials
Procedures
Methods
Information
People
Skills
Products
Services
Information
Paperwork
Voice Of Process: Feedback
Voice Of Customer: Feedback
Process
77
such a system, how to set one up and successfully implement it. Once the strategic
direction for the organization’s quality journey has been set, it needs Performance
Measures to monitor and control the journey, and to ensure the desired level of
performance is being achieved and sustained. They can, and should be established at all
levels in the organization, ideally being cascaded down and most effectively undertaken
as team activities and this is discussed in the section on Performance.
Activity 7.1. Time Allowed: 1 hour
Take a moment to study the building blocks of TQM, upon doing this, get a broadsheet or
cardboard paper and make a sketch of the building blocks of TQM with the arrows
indicating different activities.
Activity 7.1. Feedback
I expect you to provide a replica of what you studied before embarking on the activity.
Summary of Session 7
In this lecture, you have learned that;
1. Total Quality Management (TQM) in the form of statistical quality control was
invented by Walter A. Shewhart.
2. TQM in education surfaced in 1988 at Mt. Edgecombe High school in Sitka,
Alaska, when David Langford, the school’s technology teacher/coordinator,
applied Total Quality concepts in his classes.
3. Total Quality Management (TQM) refers to management methods used to enhance
quality and productivity in profit making organizations.
4. Total Quality Management (TQM) describes a management approach to long–
term success through customer satisfaction.
5. Like many of these other systems, TQM provides a framework for implementing
effective quality and productivity initiatives that can increase the profitability and
competitiveness of organizations.
78
6. The elements of TQM are; customer-focused; total employee involvement;
process-centered; integrated system; strategic and systematic approach; continual
improvement; fact-based decision making; and communication.
7. The building blocks of TQM are: processes, people, management systems and
performance measurement.
8. TQM practice involves activities related to all personnel in organization (HR), in
manufacturing, marketing, engineering, research and development (R&D), sales,
purchasing etc. Total Quality Management can be summarized as a management
system for a customer-focused organization that involves all employees in
continual improvement. It uses strategy, data, and effective communications to
integrate the quality discipline into the culture and activities of the organization.
Self-Assessment Questions (SAQs) for Session 7
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 7.1. (tests learning outcome 7.1.)
In the statements provided below, fill the blanks with the appropriate keywords
a. _________ is the transformation of a set of inputs, which can include action,
methods and operations, into the desired outputs, which satisfy the customers’
needs and expectations
b. __________ covers how to prioritize and select the right process for improvement.
c. The management methods used to enhance quality and productivity in profit
making organizations is known as _________.
d. TQM framework can improve _________ and ________ in an in a profit-making
organization.
e. _______, ________ are aspects of TQM principles.
SAQ 7.2. (tests learning outcome 7.2.)
Using the knowledge gained in this lecture, identify at least 3 major pioneers in the
development of TQM.
79
SAQ 7.3. (tests learning outcome 7.3.)
You have been chosen to make a class presentation as part of your continuous assessment
tests on the topic “The Relevance of TQM in any Organization”. Briefly give a highlight
of points to be raised in the presentation.
SAQ 7.4. (tests learning outcome 7.4.)
Total quality management can be summarized as a management system for a customer-
focused organization that involves all employees in continual improvement. Using this
background statement as an aid, identify other key elements in TQM.
SAQ 7.4. (tests learning outcome 7.4.)
In designing TQM for an educational system, outline at least 6 models that can be
adopted in getting this done.
References
Ali, N. A. & Zairi, M. 2005 Service Quality in Higher Education. Bradford University
School of Management, Bradford.
Mukhopadahyay, M. 2006 Total Quality Management in Education. Sage, New Delhi.
Thakkar, J., Deshmukh, S. G. & Shastree, A. 2006 Total quality management (TQM) in
self-financed technical institutions: a quality function deployment (QFD) and
force field analysis approach. Quality Assurance in Education 14, 1, 54-74
80
Study Session Eight: Resource Allocation/Assignment: Hungarian
Method
Expected duration: 1 week or 2 contact hours
Introduction
You are welcome back from our lecture on TQM, I want to believe that you are now a
TQM expert. This is lecture 18 titled “Hungarian method in resource allocation”. Other
methods will also be considered in the coming lectures. A special type of problem called
the assignment problem is also an allocation problem. Here we have n jobs to perform
with n persons and the problem is how to distribute the jobs to the different persons
involved. Depending on the intrinsic capacity, merit or potential of the individual to be
able to accomplish the task in different times. Then the objective function in assigning
the different jobs to different persons is to find the optimal assignment that will minimize
the total time taken to finish all the jobs by the individuals. For example, we have four
different building activities say, construction of a hotel, a theatre, a hospital and a
multistoried building and there are four contractors competing for these jobs. Each
contractor must be assigned only one job. The allocation should aim to minimize the total
time taken to complete the construction of all four activities after assigning only one job
to one individual.
Learning Outcomes for Study Session 8
At the end of this lecture, it is expected that you will be able to;
8.1. Describe the Hungarian Method in resource allocation.(SAQ 8.1)
8.2. Identify the steps in minimization and maximization of assignment
problem. (SAQ 8.2)
8.3. Calculate minimization and maximization cost in assignment problem.
(SAQ 8.3)
81
8.1. Meaning and Hungarian Method of Resource Allocation
8.1.1. Meaning of Resource Allocation
There are problems where certain facilities must be assigned to specified jobs to
maximize the overall performance of the assignment. The Hungarian Method can also
solve such assignment problems, as it is easy to obtain an equivalent minimization
problem by converting every number in the matrix to an opportunity loss. The conversion
is accomplished by subtracting all the elements of the given matrix from the highest
element. It turns out that minimizing opportunity loss produces the same assignment
solution as the original maximization problem.
8.1.2. Hungarian Method for Solving Assignment Problem
Hungarian method can be used in minimizing and the maximizing assignment problem.
Let us consider the two approaches;
1. Minimization of assignment problem
Example 8.1
A departmental head has four subordinates, and four tasks to be performed. The
subordinates differ in efficiency, and the tasks differ in their intrinsic difficulty. His
estimate, of the time each man would take to perform each task, is given the matrix below.
Men
Person 1 2 3 4
A 18 26 17 11
B 13 28 14 26
C 38 19 18 15
D 19 26 24 10
Solution to Example 8.1:
Step 1
Identify the minimum element in each row and subtract it from every element of
that row, we get the reduced matrix.
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Men
Person 1 2 3 4
A 7 15 6 0
B 0 15 1 13
C 23 4 3 0
D 9 16 14 0
Step 2
Identify the minimum element in each column and subtract it from every element of that column.
Men
Person 1 2 3 4
A 7 11 5 0
B 0 11 0 13
C 23 0 2 0
D 9 12 13 0
Step 3
Make the assignment for the reduced matrix obtain from steps 1 and 2 in the
following way:
Now proceed as in the previous example.
Optimal assignment is: A→G, B → E, C →F and D→ H
The minimum total time for this assignment scheduled is 17 +13+19+10 or 59 man-
hours.
Box 8.1. Hungarian Method in Resource Allocation
In a situation whereby certain facilities must be assigned to specified jobs to maximize
the overall performance of the assignment, the Hungarian Method can solve such
assignment problems, as it is easy to obtain an equivalent minimization problem by
converting every number in the matrix to an opportunity loss. The conversion is
accomplished by subtracting all the elements of the given matrix from the highest
element. It turns out that minimizing opportunity loss produces the same assignment
solution as the original maximization problem.
Let us also consider the other approach. We have;
2. Maximization of assignment problem
The Hungarian Method: The following algorithm applies the above theorem to a given n
× n cost matrix to find an optimal assignment. The steps needed are;
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Step 1: Subtract the smallest entry in each row from all the entries of its row.
Step 2: Subtract the smallest entry in each column from all the entries of its column.
Step 3: Draw lines through appropriate rows and columns so that all the zero entries of
the cost matrix are covered and the minimum number of such lines is used.
Step 4: Test for Optimality:
a. If the minimum number of covering lines is n, an optimal assignment of
zeros is possible and we are finished.
b. If the minimum number of covering lines is less than n, an optimal
assignment of zeros is not yet possible. In that case, proceed to Step 5.
Step 5: Determine the smallest entry not covered by any line. Subtract this entry from
each uncovered row, and then add it to each covered column. Return to Step 3.
Example 8.2
You work as a sales manager for a toy manufacturer, and you currently have three sales
people on the road meeting buyers. Your salespeople are in Kano, KW; Lagos, IKJ; and
Enugu, COAL. You want them to fly to three other cities: Ibadan, IB; Abuja, ABJ; and
Kaduna, KDN. The table below shows the cost of airplane tickets in dollars between
these cities.
From / To Ibadan Abuja Kaduna
Kano 250 400 350
Lagos 400 600 350
Enugu 200 400 350
Where should you send each of your salespeople to minimize airfare?
Solution to example 8.2
Step 1: Subtract 250 from Row 1, 350 from Row 2, and 200 from Row 3.
Step 2: Subtract 0 from Column 1, 150 from Column 2, and 0 from Column 3.
250 400 350
400 600 350
200 400 250
0 150 100
50 250 0
0 200 50
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Step 3: Cover all the zeros of the matrix with the minimum number of horizontal or
vertical
lines.
Step 4: Since the minimal number of lines is 3, an optimal assignment of zeros is
possible and we are finished.
Since the total cost for this assignment is 0, it must be an optimal assignment.
Here is the same assignment made to the original cost matrix.
0 150 100
50 250 0
0 200 50
0 150 100
50 250 0
0 200 50
0 0 100
50 100 0
0 50 50
250 400 350
400 600 350
200 400 250
0 150 100
50 250 0
0 200 50
85
Box 8.1. Steps in Minimization and Maximization of Assignment Problem using
Hungarian Method.
For Minimization;
STEP 1: Identify the minimum element in each row and subtract it from every element of
that row, we get the reduced matrix.
STEP 2: Identify the minimum element in each column and subtract it from every
element of that column
STEP 3: Make the assignment for the reduced matrix obtain from steps 1 and 2
For Maximization;
STEP 1: Subtract the smallest entry in each row from all the entries of its row.
STEP 2: Subtract the smallest entry in each column from all the entries of its column.
STEP 3: Draw lines through appropriate rows and columns so that all the zero entries of
the cost matrix are covered and the minimum number of such lines is used.
STEP 4: Test for Optimality: If the minimum number of covering lines is n, an optimal
assignment of zeros is possible and we are finished. If the minimum number of covering
lines is less than n, an optimal assignment of zeros is not yet possible. In that case,
proceed to Step 5.
STEP 5: Determine the smallest entry not covered by any line. Subtract this entry from
each uncovered row, and then add it to each covered column. Return to Step 3.
Let us consider this second example on maximization of assignment problem
Example 8.3:
Pearson
Counter A B C D E
1 30 37 40 28 40
2 40 24 27 21 36
3 40 32 33 30 35
4 25 38 40 36 36
5 29 62 41 34 39
How should the counters be assigned to persons tomaximize the profit?
Solution to Example 8.3
Here, the highest value is 62. So, we subtract each value from 62. The conversion is shown in the
following table.
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Pearson
Counter A B C D E
1 10 3 8
2 16 13 15 4
3 8 7 6 5
4 15 2 4
5 33 21 24 23
Draw the minimum number of vertical and horizontal lines necessary to cover all the
zeros in the reduced matrix.
Pearson
Counter A B C D E
1 10 3 8
2 16 13 15 4
3 8 7 6 5
4 15 2 4
5 33 21 24 23
Draw the minimum number of vertical and horizontal lines necessary to cover all the
zeros in the reduced matrix.
Select the smallest element from all the uncovered elements, i.e., 4. Subtract this element
from all the uncovered elements and add it to the elements, which lie at the intersection
of two lines. Thus, we obtain another reduced matrix for fresh assignment. Repeating step
3, we obtain a solution which is shown in the following table.
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Final Table: Maximization Problem
Pearson
Counter A B C D E
1 14 3 8
2 12 9 11
3 4 3 2 1
4 19 2 4
5 37 21 24 23
The total cost of assignment = 1C + 2E + 3A + 4D + 5B
Substituting values from original table:
40 + 36 + 40 + 36 + 62 = 214.
Take note of this point to be discussed afterwards.
Prohibited Assignment
Sometimes it may happen that a resource (say a man or machine) cannot be assigned to
perform aa activity. In such cases, the cost of performing that activity by a resource is
very high (written as M or ∞) to prohibit the entry of this pair of resource-activity into the
final solution.
Summary of Session 8
In this lecture, you have learned that;
1. There are problems where certain facilities must be assigned to specified jobs to
maximize the overall performance of the assignment. The Hungarian Method can
also solve such assignment problems, as it is easy to obtain an equivalent
minimization problem by converting every number in the matrix to an opportunity
loss.
2. Suppose we have n resources to which we want to assign to n tasks on a one-to-
one basis and if we know the cost of assigning a given resource to a given task and
wish to find an optimal assignment–one which minimizes total cost. This
Mathematical Model ca be used: Let ci,j be the cost of assigning the ith resource to
the jth task. We define the cost matrix to be the n × n matrix
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C =
3. An assignment is a set of n entry positions in the cost matrix, no two of which lie
in the same row or column. The sum of the n entries of an assignment is its cost.
An assignment with the smallest possible cost is called an optimal assignment.
4. The Hungarian Method: The Hungarian method (see above) is an algorithm which
finds an optimal assignment for a given cost matrix.
Self-Assessment Questions (SAQs) for Session 8
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 8.1. (tests learning outcome 8.1.)
How would you describe the Hungarian Method in resource allocation?
SAQ 8.2. (tests learning outcome 8.2.)
Based on what you have learnt in this lecture, identify the steps needed in minimization
and maximization of problem assignment in Hungarian Method.
C1,1 C1,2
C1,3
C2,1 C2,2C1,n
⁞ ⁞ ⁞
C C
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SAQ 8.3. (tests learning outcome 8.3.)
1. A job has four men available for work on four separate jobs. Only one man can
work on any one job. The cost of assigning each man to each job is given in the
following table. The objective is to assign men to jobs such that the total cost of
assignment is minimum.
Job
Person 1 2 3 4
A 20 25 22 28
B 15 18 23 17
C 19 17 21 24
D 25 23 24 24
Calculate the minimum cost of assignment.
2. Five different machines can do any of the five required jobs, with different profits
resulting from each assignment as given below:
Machines
Jobs A B C D E
1 30 37 40 28 40
2 40 24 27 21 36
3 40 32 33 30 35
4 25 38 40 36 36
5 29 62 41 34 39
Using the Hungarian Method, solve the above problem. Find out the maximum
profit possible through optimum assignment?
References
Hira, D.S. 2004; Operation Research, S.Chand & Company Ltd., New Delhi.
Taha, H A, 2003; Operation Research - An Introduction, Prentice Hall of India, 7th
edition.
Ravindran, Phillips and Solberg, Operations Research: Principles and Practice, John
Wiely & Sons, 2nd Edition
90
Study Session Nine: Resource Allocation/Assignment:
Transportation Problem I (Simplex and
Transportation Method)
Expected duration: 1 week or 2 contact hours
Introduction
This is another method in resource allocation. In a transportation problem, we have
certain origins which may represent factories where we produce items and supply a
required quantity of the products to a certain number of destinations. This must be done
in such a way as to maximize the profit or minimize the cost. Thus, we have the places of
production as origins and the places of supply as destinations. Sometimes the origins and
destinations are also termed as sources and sinks. The transportation problem is
concerned with finding the minimum cost of transporting a single commodity from a
given number of sources (e.g. factories) to a given number of destinations (e.g.
warehouses). The data of the model include; the level of supply at each source and the
amount of demand at each destination and the unittransportation cost of the commodity
from each source to each destination.A transportation problem can be solved by two
methods, using (a) Simplex Method and (b) Transportation Method. We shall illustrate
this with the aid of an example in the course of the lecture.
Learning Outcomes for Study Session 9
At the end of this lecture, it is expected that you will be able to;
9.1. Define and use correctly keywords printed in bold. (SAQ 9.1.)
9.2. Describe Transportation problem and its types. (SAQ 9.2)
9.3. State the variants of simplex method. (SAQ 9.3)
9.4. Highlight the steps in transportation method.(SAQ 9.4)
Key words;demand and supply
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9.1. Meaning of Transportation Problem
The transportation problem and cycle canceling methods are classical in optimization.
The usual attributions are to the 1940's and later. However, Tolsto (1930) was a pioneer
in operations research and hence wrote a book on transportation planning which was
published by the National Commissariat of Transportation of the Soviet Union, an article
called Methods of ending the minimal total kilometrage in cargo-transportation planning
in space, in which he studied the transportation problem and described a number of
solution approaches, including the, now well-known, idea that an optimum solution does
not have any negative-cost cycle in its residual graph.
The transportation problem is concerned with finding an optimal distribution plan for a
single commodity. A given supply of the commodity is available at a number of sources,
there is a specified demand for the commodity at each of the destinations, and the
transportation cost between each source-destination pair is known. In the simplest case,
the unit transportation cost is constant.
Transportation Problem (TP) is based on supply and demand of commodities transported
from several sources to the different destinations. The sources from which we need to
transport refer the supply while the destination where commodities arrive referred the
demand. It has been seen that on many occasion, the decision problem can also be
formatted as TP. In general, we try to minimize total transportation cost for the
commodities transporting from source to destination. There are two types of
Transportation Problem namely:
1. Balanced Transportation Problem and
2. Unbalanced Transportation Problem.
In-text Question
• What do you think is the major concern of transportation problem?
o The transportation problem is concerned with finding an optimal distribution
plan for a single commodity.
Now let us consider the two problems earlier mentioned one after the other.
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1. Balanced Transportation Problem: A Transportation Problem is said to be balanced
transportation problem if total number of supply is same as total number of demand.
Solution of the transportation problem
A balanced transportation problem has Total supply = Total demand which can be
expressed as
Σmi ai= Σn bj …..(eq….1)
t =1 j=1
A consequence of this is that the problem is defined by n + m - 1 supply and demand
variables since, if ai, i = 2; 3; : : : ;m and bj , j = 1; 2; : : : ; n are specified, then a1 can
be found from (eq…...1). This means that one of the constraint equations is not required.
Thus, a balanced transportation model has n + m - 1 independent constraint equations.
Since the number of basic variables in a basic solution is the same as the number of
constraints, solutions of this problem should have n + m - 1 basic variables which are
non-zero and all the remaining variables will be non-basic and thus have the value zero.
On the other hand, we also have;
2. Unbalanced Transportation Problem: A Transportation Problem is said to be
unbalanced transportation problem if total number of supply is not same as total
number of demand.
Box 9.1. The Basis of Transportation Model
Transportation Problem (TP) is based on supply and demand of commodities transported
from several sources to the different destinations. The sources from which we need to
transport refer the supply while the destination where commodities arrive referred the
demand. There are two types of Transportation Problem namely:
(1) Balanced Transportation Problem and
(2) Unbalanced Transportation Problem.
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Example 1: Balanced transportation model.
Consider the following problem with 2 factories and 3 warehouses:
Warehouse 1 Warehouse 2 Warehouse 3 Supply
Factory 1 c11 c12 c13 20
Factory 2 c21 c22 c23 10
Demand 7 10 13
Total supply = 20 + 10 = 30
Total demand = 7 + 10 + 13 = 30
= Total supply
Since Total supply = Total demand, the problem is balanced.
Example 2: Unbalanced transportation model
There are two cases to consider, namely excess demand and excess supply.
The First Case
Suppose the demand at warehouse 1 above is 9 units. Then the total supply and total
demand are unequal, and the problem is unbalanced. In this case, it is not possible to
satisfy all the demand at each destination simultaneously.We reformulate the model as
follows: since demand exceeds supply by 2 units, we introduce a dummy source (i.e. a
fictitious factory) which has a capacity of 2. The amount shipped from this dummy
source to a destination represents the shortage quantity at that destination.
It is necessary to specify the costs associated with the dummy source. There are two
situations to consider. These are;
a. Since the source does not exist, no shipping from the source will occur, so the unit
transportation costs can be set to zero.
b. Alternatively, if a penalty cost, P, is incurred for every unit of unsatisfied
demand, then the unit transportation costs should be set equal to the unit penalty
costs.
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Warehouse 1 Warehouse 2 Warehouse 3 Supply
Factory 1 c11 c12 c13 20
Factory 2 c21 c22 c23 10
Dummy P P P 2
Demand 7 10 13
In effect, we are allocating the shortage to different destinations.
Second Case
If supply exceeds demand, then a dummy destination is added which absorbs the surplus
units. Any units shipped from a source to a dummy destination represent a surplus at that
source. Again, there are two cases to consider for how the unit transportation costs should
be determined. These are;
(a) Since no shipping takes place, the unit transportation costs can be set to zero.
(b) If there is a cost for storing, S, the surplus production then the unit transportation
costs should be set equal to the unit storage costs.
Warehouse 1 Warehouse 2 Warehouse 3 Dummy Supply
Factory 1 c11 c12 c13 S 20
Factory 2 c21 c22 c23 S 10
Demand 7 10 13 4
Here we are allocating the excess supply to the different destinations.
From now on, we will discuss balanced transportation problems only, as any unbalanced
problem can always be balanced according to the above constructions.
Example 9.1:
A transportation tableau is given below. Each cell represents a shipping route (which is
an arc on the network and a decision variable in the LP formulation), and the unit
shipping costs are given in an upper right hand box in the cell.
D1 D2 D3 Supply
S1 15 30 20 50
S2 30 40 35 30
Demand 25 45 10
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To solve the transportation problem by its special purpose algorithm, the sum of the
supplies at the origins must equal the sum of the demands at the destinations (Balanced
transportation problem).
• If the total supply is greater than the total demand, a dummy destination is added
with demand equal to the excess supply, and shipping costs from all origins are
zero.
• Similarly, if total supply is less than total demand, a dummy origin is added. The
supply at the dummy origin is equal to the difference of the total supply and the
total demand.
The costs associated with the dummy origin are equal to zero.
When solving a transportation problem by its special purpose algorithm, unacceptable
shipping routes are given a cost of +M (a large number).
9.2. Variants of the Simplex Method
In this section, we present certain complications encountered in the application of the
simplex method and how they are resolved. These are called the variants of simplex
method. We can illustrate the typical cases through numerical examples. The following
variants are being considered.
i. Minimization
ii. Inequality in the wrong direction
iii. Degeneracy
iv. Unbounded solution
v. Multiple solutions
vi. Non-existing feasible solution
vii. Unrestricted variables
9.2.1. Simplex Method
The simplex method generates a sequence of feasible iterates by repeatedly moving from
one vertex of the feasible set to an adjacent vertex with a lower value of the objective
function. When it is not possible to find an adjoining vertex with a lower value, the
current vertex must be optimal, and termination occurs.
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Example 9.2:
A firm owns facilities at six places. It has manufacturing plants at places A, B and C with
daily production of 50, 40 and 60 units respectively. At point D, E and F it has three
warehouses with daily demands of 20, 95 and 35 units respectively. Per unit shipping
costs are given in the following table. If the firm wants to minimize its total
transportation cost, how should it route its products?
Warehouse
D E F
Plant
A 6 4 1
B 3 8 7
C 4 4 2
Using the Simplex Method,
The given problem can be expressed as an LPP as follows:
Let xij represent the number of units shipped from plant i to warehouse j. Let Z
representing the total cost, it can state the problem as follows.
The objective function is to,
Minimise Z = 6x11+4x12+1x13+3x21+8x22+7x23+4x31+4x32+2x33
Subject to constrains:
x11+x12+x13 =50 x11+x21+x31 =20
x21+x22+x23 =40 x12+x22+x32 =95
x31+x32+x33 =60 x13+x23+x33=35
xij≥0 for i=1,2,3 and j=1,2,3
Using Simplex method, the solution is going to be very lengthy and a cumbersome
process because of the involvement of a large number of decision and artificial variables.
Hence, for an alternate solution, procedure called the transportation method which is an
efficient one that yields results faster and with less computational effort.
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9.2.2. Transportation Method
The transportation method consists of the following three steps.
1. Obtaining an initial solution, and making an initial assignment in such a way that a
basic feasible solution is obtained.
2. Ascertaining whether it is optimal or not, by determining opportunity costs
associated with the empty cells, and if the solution is not optimal.
3. Revising the solution until an optimal solution is obtained.
9.2.3. Methods for Obtaining Basic Feasible Solution for Transportation Problem
The first step in using the transportation method is to obtain a feasible solution, namely,
the one that satisfies the rim requirements (i.e. the requirements of demand and supply).
The initial feasible solution can be obtained by several methods. The commonly used are:
i. North – west Corner Method
ii. Least Cost Method (LCM)
iii. Vogel’s Approximation Method (VAM)
These will be discussed in subsequent chapters.
Summary of Session 9
In this lecture, you have learned that;
1. The transportation problem is concerned with finding the minimum cost of
transporting a single commodity from a given number of sources (e.g. factories) to
a given number of destinations (e.g. warehouses). The data of the model include;
the level of supply at each source and the amount of demand at each destination
and the unittransportation cost of the commodity from each source to each
destination.
2. A transportation problem can be solved by two methods. These are;
a. Simplex Method and
b. Transportation Method.
• North – west Corner Method
• Least Cost Method (LCM)
� Vogel’s Approximation Method (VAM)
98
Self-Assessment Questions (SAQs) for Session 9
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 9.1. (tests learning outcome 9.1.)
Fill the blanks in the statement provided below with the appropriate keywords
In the basis of transportation problem, the sources from which we need to transport refer
the _______ while the destination where commodities arrive referred the _________.
SAQ 9.2. (tests learning outcome 9.2.)
Based on what you have learnt in this lecture, shed more light on transportation problem
by laying emphasis on the types.
SAQ 9.3. (tests learning outcome 9.3.)
Identify some of the variants of simplex method in transportation problem.
SAQ 9.4. (tests learning outcome 9.4.)
In adopting a transportation method for resource allocation, what are some of those steps
you need to keep yourself abreast of?
References
Hira, D.S. 2004; Operation Research, S.Chand & Company Ltd., New Delhi.
Taha, H A, 2003; Operation Research - An Introduction, Prentice Hall of India, 7th
edition.
Ravindran, Phillips and Solberg, Operations Research : Principles and Practice, John
Wiely & Sons, 2nd Edition
99
Study Session Ten: Resource Allocation/Assignment: Transportation
Problem II (North-West Rule Model)
Expected duration: 1 week or 2 contact hours
Introduction
You are welcome back to EME 302 class. This lecture is a continuation of the topic we
started in the last 2 lectures. I urge you follow along as usual. The North-West rule is
another transportation method used solving problems most especially in determining the
feasible solution of transportation problems
Learning Outcomes for Study Session 10
At the end of this lecture, it is expected that you will be able to;
10.1. State the steps involved in the use of NWCR.(SAQ 10.1)
10.2. Determine the initial feasible solution by North West Corner Method.
(SAQ 10.2)
10.1. Overview and Meaning of the North-West Rule Model (NWRM)
10.1.1. Overview of the North-West Rule Model
The method is the simplest but most inefficient as it has the highest total transportation
cost in comparison to all other methods. The main reason that can be attributed to this is
that the method does not consider the cost of transportation for all the possible alternative
routes.
10.1.2. North-West Corner Method (NWCM)
The North-West Corner Rule or North-West Rule Model is a method for computing a
basic feasible solution of a transportation problem where the basic variables are selected
from the North – West corner (i.e., top left corner).
As we proceed in this lecture, let us examine the steps involved in this method. These are;
100
1. Select the north west (upper left-hand) corner cell of the transportation table and
allocate as many units as possible equal to the minimum between available supply
and demand requirements, i.e., min (s1, d1).
2. Adjust the supply and demand numbers in the respective rows and columns
allocation.
3. If the supply for the first row is exhausted, then move down to the first cell in the
second row.
4. If the demand for the first cell is satisfied, then move horizontally to the next cell
in the second column.
5. If for any cell supply equals demand, then the next allocation can be made in cell
either in the next row or column.
6. Continue the procedure until the total available quantity is fully allocated to the
cells as required.
Box 10.1. North West Corner Method (NWCM)
The North-West Corner Rule or North-West Rule Model is a method for computing a basic feasible
solution of a transportation problem where the basic variables are selected from the North – West corner
(i.e., top left corner).
Example 10.1:
Basic Feasible Solution Using North-West Corner Method
Table 10.1
Warehouse
D E F
Plant
A 6 4 1
B 3 8 7
C 4 4 2
The table 10.2 above this leads to table 10.2 below
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Table 10.2
From To D E F Supply
A
6
4
1 50
B 3
8
7 40
C 4
4
2
60
Demand 20 95 35 150
Total Cost: (6*20) + (4*30) + (8*40) + (4*25) + (2*35) = N730
This routing of the units meets all the rim requirements and entails 5 (=m+n-1 =3+3-1)
shipments as there are 5 occupied cells; It involves a total cost of N730.
Consider the problem represented by the following transportation tableau. The number in
the bottom right of cell (i; j) is cij, the cost of transporting 1 unit from source i to
destination j. Values of xij, the quantity actually transported from source i to estimation j,
will be entered in the top left of each cell. Note that there are 3 factories and 4
warehouses and so m = 3, n = 4.
W1 W2 W3 W4 Supply
F1 10 0 20 11 20
F2 12 7 9 20 25
F3 0 14 16 18 15
Demand 10 15 15 20
For the above example:
• x11 = 10. Cross out column 1. The amount left in row 1 is 10.
• x12 = 10. Cross out row 1. 5 units are left in column 2.
• x22 = 5. Cross out column 2. 20 units are left in row 2.
• x23 = 15. Cross out column 3. 5 units are left in row 2.
20 30
40
25 35
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Only column 4 is now left and so both the remaining variables x24 and x34 will be basic.
The only feasible allocation of the 5 units in row 2 and the 15 units in row 3is to allocate
x24 = 5 and x34 = 15, which also ensures that the demand in column 4 is satisfied.
This provides the initial basic feasible solution x11 = 10, x12 = 10, x22 = 5, x23 = 15, x24 = 5,
x34 = 15. The remaining variables are non-basic and therefore equal to zero.
They must always add up to the total supply and demand in each row and column.
Note that some books position the data differently in the cells of the table.
Example10.2:
Solve the Transportation Table to find Initial Basic Feasible Solution using North-West Corner Method.
Total Cost =19*5+30*2+30*6+40*3+70*4+20*14
= N1015
Supply
19 30 50 10
5 2
70 30 40 60
6 3
40 8 70 20
4 14
Demand 34
S1
S2
S3
7
9
18
5 8 7 14
D1 D2 D3 D4
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Initial table developed using Northwest Corner Method
Total Cost = 12(400)+13(100)+4(700)+9(100) +12(200) +4(500) = 142,000
Summary of Session 10
In this lecture, you have learned that;
1. The North-West Corner Rule or North-West Rule Model is a method for
computing a basic feasible solution of a transportation problem where the basic
variables are selected from the North – West corner (i.e., top left corner).
2. The North-West Corner Methodgenerates an initial allocation according to the
following procedure:
• Allocate the maximum amount allowable by the supply and demand
constraints to the variable x11 (i.e. the cell in the top left corner of the
transportation tableau).
• If a column (or row) is satisfied, cross it out. The remaining decision
variables in that column (or row) are non-basic and are set equal to zero. If
a row and column are satisfied simultaneously, cross only one out (it does
not matter which).
• Adjust supply and demand for the non-crossed out rows and columns.
• Allocate the maximum feasible amount to the first available non-crossed
out element in the next column (or row).
• When exactly one row or column is left, all the remaining variables are
basic and are assigned the only feasible allocation.
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Self-Assessment Questions (SAQs) for Session 10
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 10.1. (tests learning outcome 10.1.)
Identify the steps needed to guide you in the usage of the North-West Corner Rule or
North-West Rule Model.
SAQ 10.2. (tests learning outcome 10.2.)
1. The NWCR algorithm applied to this problem resulted to the following table for questions 1 to 3:
Destination
Plant X Y W Z Supply
A 21 18 27 22 50
B 19 18 24 20 60
C 24 25 28 25 50
Demand 50 70 30 10 160
Using the North-West corner method;
a. find the total cost?
b. What is allocated to cell X11?
c. What is the allocated to cell X34?
2. Determine the initial feasible solution by North West Corner Method
Factory Warehouse Factory
Capacities A B C D E
X 5 8 6 4 3 800
Y 4 7 8 6 5 600
Z 8 4 7 5 6 1100
Warehouse
Requirements
350 425 500 650 575 2500
Using the North-West corner method, find the total cost?
105
References
Ahmad, Hlayel Abdallah. 2012 "The Best Candidates Method for Solving Optimization
Problems." Journal of Computer Science, 711-715.
Sudhakar, V.J, Arunnsankar N, Karpagam T. 2012. A new approach for find an Optimal
Solution for Trasportation Problems, European Journal of Scientific Research 68
254-257.
Turkey, Mertin. 2008 "NEW ALTERNATE METHODS OF TRANSPORTATION."
transportation problem, 1008-1012.
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Study Session Eleven: Resource Allocation/Assignment: Least-Cost
Method
Expected duration: 1 week or 2 contact hours
Introduction
Hello, I hope you have been getting equipped with the skills and steps needed when using
the Transportation Problem in resource allocation. In the last lecture, we examined the
North-West Corner Model (NWCM) used in solving problems most especially in
determining the feasible solution of transportation problems. As we continue our
discussion on this topic, the method we are examining now is the Least-cost method
which is another transportation method used in solving problems most especially in
determining the feasible solution of transportation problems.
Learning Outcomes for Study Session 11
At the end of this lecture, it is expected that you will be able to;
11.1. State the steps involved in the use of Least-cost Method.(SAQ 11.1.)
11.3. Determine the feasible solution of transportation problems in Least-cost
method in solving resource allocation problems.(SAQ 11.2.)
11.1. Least Cost Method in Resource Allocation
Least-Cost Method is also known as Minimum Cell-Cost Method or as the Matrix
Minima Methods.This method usually provides a better initial basic feasible solution than
the North-West Corner method since it considers the cost variables in the problem.
Let us consider the steps in the method. We have;
1. Assign as much as possible to the cell with the smallest unit cost in the entire
table. If there is a tie, then choose arbitrarily.
2. Cross out the row or column which has satisfied supply or demand. If a row and
column are both satisfied, then cross out only one of them.
3. Adjust the supply and demand for those rows and columns which are not crossed
107
out.
4. When exactly one row or column is left, all the remaining variables are basic and
are assigned the only feasible allocation.
Example 11.1
W1 W2 W3 W4 Supply
F1 10 0 20 11 20
F2 12 7 9 20 25
F3 0 14 16 18 15
Demand 10 15 15 20
For the above example:
• Cells (1; 2) and (3; 1) both have zero cost so we arbitrarily choose the first and
assign
• x12 = 15. Cross out column 2. The amount left in row 1 is 5.
• x31 = 10. Cross out column 1. The amount left in row 3 is 5.
• x23 = 15. Cross out column 3. The amount left in row 2 is 10.
• Only column 4 is now left and so all the variables in this column will be basic. The
• Only feasible allocation is x14 = 5, x24 = 10 and x34 = 5.
This provides the initial basic feasible solution x12 = 15, x31 = 10, x23 = 15, x14 = 5, x24 =
10, x34 = 5. All the other variables are non-basic and are therefore equal to zero.
Again, we have 6 basic variables as required.
In-text Question
• What are the other names used instead of the Least-cost Method?
o It is also known as Minimum Cell-Cost Method or as the Matrix Minima
Methods.
At this point, let us also examine the minimum cell-cost method
11.1.1. Minimum Cell-Cost Method
Although the North-west Corner Rule is the easiest, it is not the most attractive because our objective is
not included in the process.
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Steps of Minimum Cell-Cost Method
The steps involved in this method are;
1. Select the cell with the minimum cell cost in the tableau and allocate as much to
this cell as possible, but within the supply and demand constraints.
2. Select the cell with the next minimum cell-cost and allocate as much to this cell as
possible within the demand and supply constraints.
3. Continue the procedure until all the supply and demand requirements are satisfied.
In a case of tied minimum cell-costs between two or more cells, the tie can be
broken by selecting the cell that can accommodate the greater quantity.
Initial tableau developed using Minimum Cell-Cost Method
Total Cost = 12(300)+4(200)+4(700)+10(100)+9(200)+4(500)= 120,000
Box 11.1. Steps in Least- cost method of Resource Allocation
The steps here are;
1. Assign as much as possible to the cell with the smallest unit cost in the entire table. If
there is a tie, then choose arbitrarily.
2. Cross out the row or column which has satisfied supply or demand. If a row and
column are both satisfied, then cross out only one of them.
3. Adjust the supply and demand for those rows and columns which are not crossed out.
4. When exactly one row or column is left, all the remaining variables are basic and are
assigned the only feasible allocation.
109
11.1.2. MODI Method (for obtaining reduced costs)
Associate a number, ui, with each row and vj with each column.
The steps under this method are;
• Step 1: Set u1 = 0.
• Step 2: Calculate the remaining ui’s and vj’s by solving the relationship cij = ui +
vj for occupied cells.
• Step 3: For unoccupied cells (i,j), the reduced cost = cij – ui – vj.
Step 1: For each unoccupied cell, calculate the reduced cost by the MODI method. Select
the unoccupied cell with the most negative reduced cost. (For maximization problems
select the unoccupied cell with the largest reduced cost.) If none, STOP.
Step 2: For this unoccupied cell, generate a stepping stone path by forming a closed loop
with this cell and occupied cells by drawing connecting alternating horizontal and vertical
lines between them. Determine the minimum allocation where a subtraction is to be made
along this path.
Step 3: Add this allocation to all cells where additions are to be made, and subtract this
allocation to all cells where subtractions are to be made along the stepping stone path.
(Note: An occupied cell on the stepping stone path now becomes 0 (unoccupied). If more
than one cell becomes 0, make only one unoccupied; make the others occupied with 0′s.)
110
Refer to Step 1
Example 11.2:
Acme Block Co. (ABC)
Acme Block Company has orders for 80 tons of concrete blocks at three suburban
locations as follows: Northwood — 25 tons, Westwood — 45 tons, and Eastwood — 10
tons. Acme has two plants, each of which can produce 50 tons per week. Delivery cost
per ton from each plant to each suburban location is shown below.
How should end of week shipments be made to fill the above orders?
Since total supply = 100 and total demand = 80, a dummy destination is created with
demand of 20 and 0 unit costs.
Iteration 1: Tie for least cost (0), arbitrarily select x14. Allocate 20. Reduce s1 by 20 to
30 and delete the Dummy column.
Iteration 2: Of the remaining cells the least cost is 24 for x11. Allocate 25. Reduce s1 by
25 to 5 and eliminate the Northwood column.
Iteration 3: Of the remaining cells the least cost is 30 for x12. Allocate 5. Reduce the
Westwood column to 40 and eliminate the Plant 1 row.
Iteration 4: Since there is only one row with two cells left, make the final allocations of
40 and 10 to x22 and x23, respectively.
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Matrix minimum method is a method for computing a basic feasible solution of a
transportation problem where the basic variables are chosen according to the unit cost of
transportation.
The steps are;
1. Identify the box having minimum unit transportation cost (cij).
2. If there are two or more minimum costs, select the row and the column
corresponding to the lower numbered row.
3. If they appear in the same row, select the lower numbered column.
4. Choose the value of the corresponding xij as much as possible subject to the
capacity and requirement constraints.
5. If demand is satisfied, delete that column.
6. If supply is exhausted, delete that row.
7. Repeat steps 1-6 until all restrictions are satisfied.
Table 11.1 Basic Feasible Solution Using Least Cost Method of Example
Warehouse
D E F
Plant
A 6 4 1
B 3 8 7
C 4 4 2
The table 11.1 above this leads to table11. 2 below
Table 11.2
From To D E F Supply
A
6
4
1 50
B 3
8
7 40
C 4
4
2
60
Demand 20 95 35 150
Total Cost: 3*20 + 4*15 + 8*20 +4*60 + 1*35 = N555
This routing of the units meets all the rim requirements and entails 5 (=m+n-1 =3+3-1)
shipments as there are 5 occupied cells; It involves a total cost of N555.
20
15
20
60
35
112
Follow these steps:
Step1: Select the cell having lowest unit cost in the entire table and allocate the
minimum of supply or demand values in that cell.
Step2: Then eliminate the row or column in which supply or demand is exhausted. If
both the supply and demand values are same, either of the row or column can be
eliminated.In case, the smallest unit cost is not unique, then select the cell where
maximum allocation can be made.
Step3: Repeat the process with next lowest unit cost and continue until the entire
available supply at various sources and demand at various destinations is
satisfied.
Next
Next
Next
Supply
19 30 50 10
70 30 40 60
40 8 70 20
8
Demand 34
S3 18
5 8 7 14
S1 7
S2 9
D1 D2 D3 D4
Supply
19 50 10
7
70 40 60
40 70 20
Demand 34
D1 D3 D4
7 14
7
9
S1
S2
S3 10
5
Supply
70 40 60
40 70 20
7
Demand 34
S3 10
5 7 7
S2 9
D1 D3 D4
Supply
70 40
7
40 70
Demand 347
S2
D1 D3
9
3S3
5
113
Next
The total transportation cost obtained by this method =
8*8+10*7+20*7+40*7+70*2+40*3
= N814
Here, we can see that the Least Cost Method involves a lower cost than the North-West
Corner Method.
Summary of Session 11
In this lecture, you have learned that;
1. Least-Cost Method is also known as Minimum Cell-Cost Method.This method
usually provides a better initial basic feasible solution than the North-West Corner
method since it considers the cost variables in the problem.
2. The steps under this method are;
• Assign as much as possible to the cell with the smallest unit cost in the entire
tableau. If there is a tie, then choose arbitrarily.
• Cross out the row or column which has satisfied supply or demand. If a row
and column are both satisfied, then cross out only one of them.
• Adjust the supply and demand for those rows and columns which are not
crossed out.
• When exactly one row or column is left, all the remaining variables are basic
and are assigned the only feasible allocation.
Self-Assessment Questions (SAQs) for Session 11
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
Supply
70
2
40
3
Demand 345
S2 2
S3 3
D1
114
SAQ 11.1. (tests learning outcome 11.1.)
As an expert in resource allocation, in using the Least-cost method in determining the
feasible solution of transportation problems, what are those steps that must be followed
rigidly?
SAQ 11.2. (tests learning outcome 11.2.)
For the transportation problem given by the following table, find an initial basic feasible
solution by the least-cost method and then find an optimal solution.
Supply
2 1 3 7
4 5 6 8
Demand 5 6 4
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Study SessionTwelve: Resource Allocation/Assignment:
(Vogel’s Approximation Method)
Expected duration: 1 week or 2 contact hours
Introduction
In the last 3 lectures, we have been examining the Transportation Problem Method in
resource allocation. As stated earlier, we have different methods used in solving problems
most especially in determining the feasible solution of transportation problems. Another
approach we can also use in realising this objective is the Vogel approximation method.
In this lecture, we shall be considering Vogel approximation method and the steps needed
when working with this method.
Learning Outcomes for Study Session 12
At the end of this lecture, it is expected that you will be able to;
12.1. Outline the steps involved in the use of Vogel approximation Method.
(SAQ 12.1.)
12.2. Determine the feasible solution of transportation problems using Vogel’s
method.(SAQ 12.2.)
12.1. Vogel’s Approximation Method in Resource Allocation
Vogel approximation method is also known as the Unit Cost Penalty Method. The Vogel
approximation method is an iterative procedure for computing a basic feasible solution of
the transportation problem. Another way of finding an initial solution to problem is
through the Vogel’s Approximation method which is as simple as the North-west corner
method. It is associated with cost, which is an important concept in Educational Planning.
In addition to the northwest corner and intuitive lowest-cost methods of setting an initial
solution to transportation problems, we introduce one other important technique Vogel’s
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Approximation method(VAM). VAM is not quite as simple as the northwest corner
approach, but it facilitates a very good initial solution as a matter of fact, one that is often
the optimal solution.
Vogel’s Approximation method tackles the problem of finding a good initial solution by
considering the costs associated with each route alternative. This is something that the
northwest corner rule did not do. To apply the VAM, we first compute for each row and
column the penalty faced if we should ship over the second-bestroute instead of the least-
cost route.Vogel’s Approximation is another method used in making decision.
The method is structured with various steps for its usage. These steps are;
1. Identify the boxes having minimum and next to minimum transportation cost in
each row and write the difference (penalty) along the side of the table against the
corresponding row.
2. Identify the boxes having minimum and next to minimum transportation cost
ineach column and write the difference (penalty) against the corresponding
column.
3. Identify the maximum penalty. If it is along the side of the table, make maximum
allotment to the box having minimum cost of transportation in that row. If it is
below the table, make maximum allotment to the box having minimum cost of
transportation in that column.
4. If the penalties corresponding to two or more rows or columns are equal, select the
top most row and the extreme left column.
In-text Question
• Do you think Vogel Approximation Method (VAM) is quite simpler that the
North-West Corner Approach?
o No, VAM is not quite as simple as the northwest corner approach, but it
facilitates a very good initial solution as a matter of fact, one that is often the
optimal solution.
117
Table 12. Basic Feasible Solution Using Vogel’s Approximation Method of Example
Warehouse
D E F
Plant
A 6 4 1
B 3 8 7
C 4 4 2
The table 12.1 leads to table 12.2 below
Table 12.2
D E F Supply Iteration
From To I II
A
6
4
1
50 3 3
B
3
8
7
40 4 1
C
4
4
2 60 2 2
Demand 20 95 35 150
I 1 0 1
II - 0 1
Total Cost: 3*20 + 4*15 + 8*20 +4*60 + 1*35 = N555
This routing of the units meets all the rim requirements and entails 5 (=m+n-1 = 3+3-1)
shipments as there are 5 occupied cells; It involves a total cost of N555.
Box 12.1. Vogel’s Approximation Method
Vogel’s Approximation method tackles the problem of finding a good initial solution by considering the
costs associated with each route alternative. This is something that the northwest corner rule did not do.
To apply the VAM, we first compute for each row and column the penalty faced if we should ship over
the second-best route instead of the least-cost route.
Other ways to get this done are;
Step1: Calculate penalty for each row and column by taking the difference between the
two smallest unit costs. This penalty or extra cost must be paid if one fails to
20 20
60
35 15
118
allocate the minimum unit transportation cost.
Step2: Select the row or column with the highest penalty and select the minimum unit
cost of that row or column. Then, allocate the minimum of supply or demand
values in that cell. If there is a tie, then select the cell where maximum allocation
could be made.
Step3: Adjust the supply and demand and eliminate the satisfied row or column. If a
row and column are satisfied simultaneously, only of them is eliminated and the
other one is assigned a zero value. Any row or column having zero supply or
demand, cannot be used in calculating future penalties.
Step4: Repeat the process until all the supply sources and demand destinations are
satisfied.
Supply Row Diff.
19 30 50 10
70 30 40 60
40 8 70 20
8
Demand 34
Col.Diff.
D4
14
S3
5 8 7
D1 D2 D3
S1
S2
21 22 10 10
9
10
12
7
9
18
Supply Row Diff.
19 50 10
5
70 40 60
40 70 20
Demand 34
Col.Diff.
9
20
20
21 10
S2 9
S3 10
5 7 14
D1 D3 D4
S1 7
10
119
The total transportation cost obtained by this method =
8*8+19*5+20*10+10*2+40*7+60*2
= N779
Here, we can see that Vogel’s Approximation Method involves the lowest cost than
North-West Corner Method and Least Cost Method and hence is the most preferred
method of finding initial basic feasible solution.
Summary ofSession 12
In this lecture, you have learned that;
1. Vogel approximation method is also known as the Unit Cost Penalty Method. The
Vogel approximation method is an iterative procedure for computing a basic
feasible solution of the transportation problem.
2. The steps in this method are;
• Step1: Calculate penalty for each row and column by taking the difference
between the two smallest unit costs. This penalty or extra cost must be paid if
one fails to allocate the minimum unit transportation cost.
Supply Row Diff.
50 10
40 60
70 20
10
Demand 34
Col.Diff.
147
S1 2
S2 9
S3 10
D3 D4
40
20
50
10 10
Supply Row Diff.
50 10
2
40 60
Demand 34
Col.Diff.
D3 D4
S1 2
S2 9
7 4
20
10 50
40
Supply Row Diff.
40 60
7 2
Demand 34
Col.Diff.
S2 9
D3 D4
7 2
20
120
• Step2: Select the row or column with the highest penalty and select the
minimum unit cost of that row or column. Then, allocate the minimum of
supply or demand values in that cell. If there is a tie, then select the cell where
maximum allocation could be made.
• Step3: Adjust the supply and demand and eliminate the satisfied row or
column. If a row and column are satisfied simultaneously, only of them is
eliminated and the other one is assigned a zero value. Any row or column
having zero supply or demand, cannot be used in calculating future penalties.
• Step4: Repeat the process until all the supply sources and demand destinations
are satisfied.
Self-Assessment Questions (SAQs) for Session 12
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 12.1. (tests learning outcome 12.1.)
Based on the knowledge you have gained in this lecture, what are some of the steps
needed when using the Vogel’s Approximation Method (VAM) in resource allocation?
SAQ 12.2. (tests learning outcome 12.2.)
1. A company has factories at F1, F2 and F3 which supply to warehouses at W1, W2 and
W3. Weekly factory capacities are 200, 160 and 90 units, respectively. Weekly
warehouse requirements are 180, 120 and 150 units, respectively. Unit shipping costs
(in Naira) are as follows:
W1 W2 W3 W4
F1 16 20 12 200
F2 14 8 18 160
F3 26 24 16 90
Demand 180 120 150 450
Using the Vogel approximation Method, Determine the optimal distribution for this
company to minimize total shipping cost.
a. 5920
121
b. 6460
c. 6600
d. None of the above
2. The following table shows all the necessary information on the availability of supply
to each warehouse, the requirement of each market and unit transportation cost (in N)
from each warehouse to each market.
Market Supply
P Q R S
Warehouse A 6 3 5 4 22
B 5 9 2 7 15
C 5 7 8 6 8
Demand 7 12 17 9 45
Determine cost value for this transportation problem by using the Vogel approximation Method.
a. 176 b. 150 c. 149 d. None of the above
References
Dwivedi, R. K., Mehta, N. N. and Dubey, O. P., 2009; Interactive Decision Making in
Prioritized Unbalanced Transportation Problems. The Icfai University Journal of
Operations Management, Vol. 8, No. 1, pp. 67-76. Available at SSRN:
http://ssrn.com/abstract=1344168
Goval, S. K. 1984, Improving VAM for unbalance transportation problems, Journal of
Operational Research Society 35, 1113-1114
Pearman, A. D., (1974) Two Errors in Quandt’s Model of Transportation and Optimal
Network Construction Journal of the Regional Science Association, 14, 281-286.
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Study Session Thirteen: Model in Education
Expected duration: 2 weeksor 4 contact hours
Introduction
I welcome you back from the series of lectures you just concluded on resource allocation.
I want to implore you to attempt the SAQs provided as practice questions to master the
skills required. For this lecture, we shall be focusing on the Models in Education. Most
operations research models are symbolic models because symbols represent properties of
the system. The earliest models were physical representations such as model ships,
airplanes, tow tanks, and wind tunnels. Physical models are usually easy to construct, but
only for relatively simple objects or systems, and are usually difficult to change. The
model is meant for organizations. For organizations that wants to focus on quality in a
systematic way. The models can be applied in any type or organization: large and small,
profit and non-profit, local and international.
Learning Outcomes for Study Session 13
At the end of this lecture, it is expected that you will be able to;
13.1. Define and use correctly keywords printed in bold. (SAQ 13.1.)
13.2. Describe the constituents of a model. (SAQ 13.2)
13.3. Identify the basic activities when deriving solutions from model. (SAQ
13.3)
13.4. Highlight the processes involved in building a model. (SAQ 13.4)
13.5. Make a list of the steps available in Lewin, Mckinsey, and Kotter’s Change
Management Model. (SAQ 13.5)
Key words; model, management model, symbolic models, analogue, physical model,
graphic model, deductive, and inductive.
123
13.1. Meaning of a Model
A model is a simplified representation of the real world and as such includes only those
variables relevant to the problem at hand. A model of freely falling bodies, for example
does not refer to the colour, texture, or shape of the body involved. Furthermore, a model
may not include all relevant variables because a small percentage of these may account
for most of the phenomenon to be explained. Many of the simplifications used produce
some error in predictions derived from the model, but these can often be kept small
compared to the magnitude of the improvement in operations that can be extracted from
them.
Please note that aManagement Model is simply the set of choices made by executives
about how the work of management gets done about how they define objectives, motivate
effort, coordinate activities, and allocate resources. The physical model takes the form of
graph, easier to construct and manipulate but more abstract. Since graphic representation
of more than three variables is difficult, symbolic models came into use. There is no limit
to the number of variables that can be included in a symbolic model, and such models are
easier to construct and manipulate than physical models.
A management model is the choices made by organisation’s top executives regarding
how they define objectives, motivate effort, coordinate activities and allocate resources;
in other words, how they define the work of management. Inspired by changes in the
expectations of their employees, new technological capabilities and the offerings of
emerging competitors, some companies are discovering that a distinctive management
model can itself be a key driver of its competitiveness.
For Symbolic models, they are completely abstract. When the symbols in a model are
defined, the model is given content or meaning. This has important consequences.
Symbolic models of systems of very different content often reveal similar structure.
Hence, most systems and problems arising in them can be fruitfully classified in terms of
relatively few structures. Furthermore, since methods of extracting solutions from models
depend only on their structure, some methods can be used to solve a wide variety of
problems from a contextual point of view. Finally, a system that has the same structure as
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another, may be different in content can be used as a model of the other. Such a model is
called an analogue. By use of such models much of what is known about the first system
can be applied to the second.Despite the obvious advantages of symbolic models there
are many cases in which physical models are still useful, as in testing physical structures
and mechanisms; the same is true for graphic models. Physical and graphic models are
frequently used in the preliminary phases of constructing symbolic models of systems.
In-text Question
• How would you describe a management model based on what you have learnt in
this lecture?
o Management Model is simply the set of choices made by executives about how
the work of management gets done, how they define objectives, motivate
effort, coordinate activities, and allocate resources.
Let us proceed on our discussion on the meaning of a model;
Operations research models represent the causal relationship between the controlled
and uncontrolled variables and system performance; they must therefore be explanatory,
not merely descriptive. Only explanatory models can provide the requisite means to
manipulate the system to produce desired changes in performance.Operations research
analysis is directed toward establishing cause-and-effect relations. Though experiments
with actual operations of all or part of a system are often useful, these are not the only
way to analyze cause and effect. There are four patterns of model construction, only two
of which involve experimentation: inspection, use of analogues, operational analysis, and
operational experiments. They are considered here in order of increasing complexity. In
some cases, the system and its problem are relatively simple and can be grasped either by
inspection or from discussion with persons familiar with it. In general, only low-level and
repetitive operating problems, those in which human behaviour plays a minor role can be
so treated.
Another point you need to register here is that, when the researcher finds it difficult to
represent the structure of a system symbolically, it is sometimes possible to establish a
similarity, if not an identity, with another system whose structure is better known and
125
easier to manipulate. It may then be possible to use either the analogous system itself or a
symbolic model of it as a model of the problem system. For example, an equation derived
from the kinetic theory of gases has been used as a model of the movement of trains
between two classification yards. Hydraulic analogues of economies and electronic
analogues of automotive traffic have been constructed with which experimentation could
be carried out to determine the effects of manipulation of controllable variables. Thus,
analogues may be constructed as well as found in existing systems.In some cases,
analysis of actual operations of a system may reveal its causal structure. Data on
operations are analyzed to yield an explanatory hypothesis which is tested by analysis of
operating data. Such testing may lead to revision of the hypothesis. The cycle is
continued until a satisfactory explanatory model is developed.
For example, an analysis of the cars stopping at urban automotive service stations located
at intersections of two streets revealed that almost all came from four of the 16 possible
routes through the intersection (four ways of entering times four ways of leaving).
Examination of the percentage of cars in each route that stopped for service suggested
that this percentage was related to the amount of time lost by stopping. Data were then
collected on time lost by cars in each route. This revealed a close inverse relationship
between the percentage stopping and time lost. But the relationship was not linear; that is,
the increases in one were not proportional to increases in the other. It was then found that
perceived lost time exceeded actual lost time, and the relationship between the percentage
of cars stopping and perceived lost time was close and linear. The hypothesis was
systematically tested and verified and a model constructed that related the number of cars
stopping at service stations to the amount of traffic in each route through its intersection
and to characteristics of the station that affect the time required to get service.
In situations where it is not possible to isolate the effects of individual variables by
analysis of operating data, it may be necessary to resort to operational experiments to
determine which variables are relevant and how they affect system performance.
Such is the case, for example, in attempts to quantify the effects of advertising (amount,
timing, and media used) upon sales of a consumer product. Advertising by the producer is
only one of many controlled and uncontrolled variables affecting sales. Hence, in many
126
cases its effect can only be isolated and measured by controlled experiments in the field.
The same is true in determining how the size, shape, weight, and price of a food product
affect its sales. In this case laboratory experiments on samples of consumers can be used
in preliminary stages, but field experiments are eventually necessary. Experiments do not
yield explanatory theories, however. They can only be used to test explanatory
hypotheses formulated before designing the experiment and to suggest additional
hypotheses to be tested.
Box 13.1. Meaning of a Model
There are four patterns of model construction, only two of which involve
experimentation: inspection, use of analogues, operational analysis, and operational
experiments. They are considered here in order of increasing complexity. In some cases,
the system and its problem are relatively simple and can be grasped either by inspection
or from discussion with persons familiar with it. In general, only low-level and repetitive
operating problems, those in which human behaviour plays a minor role can be so treated.
Another point you need to note when describing a model is that it is sometimes necessary
to modify an otherwise acceptable model because it is not possible or practical to find the
numerical values of the variables that appear in it. For example, a model to be used in
guiding the selection of research projects may contain such variables as “the probability
of success of the project,” “expected cost of the project,” and its “expected yield.” But
none of these may be calculable with any reliability. Models not only assist in solving
problems but also are useful in formulating them; that is, models can be used as guides to
explore the structure of a problem and to reveal choices that might otherwise be missed.
In many cases the course of action revealed by such application of a model is so
obviously superior to previously considered possibilities that justification of its choice is
hardly required.
In some cases, the model of a problem may be either too complicated or too large to
solve. It is frequently possible to divide the model into individually solvable parts and to
take the output of one model as an input to another. Since the models are likely to be
interdependent, several repetitions of this process may be necessary.
127
13.2.DerivingSolutionsfromModels
Another aspect of this lecture to be considered now is the derivation of solutions from
models. Procedures for deriving solutions from models are either deductive or inductive.
With deduction one moves directly from the model to a solution in either symbolic or
numerical form. Such procedures are supplied by mathematics; for example, the calculus.
An explicit analytical procedure for finding the solution is called an algorithm. Even if a
model cannot be solved, and many are too complex for solution, it can be used to
compare alternative solutions. It is sometimes possible to conduct a sequence of
comparisons, each suggested by the previous one and each likely to contain a better
alternative than was contained in any previous comparison. Such a solution-seeking
procedure is called heuristic.
Inductive procedures involve trying and comparing different values of the controlled
variables. Such procedures are said to be iterative (repetitive) if they proceed through
successively improved solutions until either an optimal solution is reached or further
calculation cannot be justified. A rational basis for terminating such a process known
as “stopping rules” involves the determination of the point at which the expected
improvement of the solution on the next trial is less than the cost of the trial. Such well-
known algorithms as linear, nonlinear, and dynamic programming are iterative
procedures based on mathematical theory. Simulation and experimental optimization are
iterative procedures based primarily on statistics.
Box. 13.2. Meaning of a Model
Models not only assist in solving problems but also are useful in formulating them; that
is, models can be used as guides to explore the structure of a problem and to reveal
choices that might otherwise be missed. In many cases the course of action revealed by
such application of a model is so obviously superior to previously considered possibilities
that justification of its choice is hardly required.
13.2.1. Testing the Model and the Solution
Let me start by asking you this question. Why do you think a model can be deficient i.e.
not serving the purpose it is meant for? A model may be deficient because it includes
128
irrelevant variables, excludes relevant variables, contains inaccurately evaluated
variables, is incorrectly structured, or contains incorrectly formulated constraints. Tests
for deficiencies of a model are statistical in nature; their use requires knowledge of
sampling and estimation theory, experimental designs, and the theory of hypothesis
testing.
Sampling-estimation theory is concerned with selecting a sample of items from a large
group and using their observed properties to characterize the group. To save time and
money, the sample taken is as small as possible. Several theories of sampling design and
estimation are available, each yielding estimates with different properties.
The structure of a model consists of a function relating the measure of performance to the
controlled and uncontrolled variables; for example, a business may attempt to show the
functional relationship between profit levels (the measure of performance) and controlled
variables (prices, amount spent on advertising) and uncontrolled variables (economic
conditions, competition). To test the model, values of the measure of performance
computed from the model are compared with actual values under different sets of
conditions. If there is a significant difference between these values, or if the variability of
these differences is large, the model requires repair. Such tests do not use data that have
been used in constructing the model, because to do so would determine how well the
model fits performance data from which it has been derived, not how well it predicts
performance.
Pause to answer this question
In-text Question
• What are some of the factors that can render a model deficient?
o A model may be deficient when it includes irrelevant variables, excludes
relevant variables, contains inaccurately evaluated variables, is incorrectly
structured, or contains incorrectly formulated constraints.
The solution derived from a model is tested to find whether it yields better performance
than some alternative, usually the one in current use. The test may be prospective, against
129
future performance, or retrospective, comparing solutions that would have been obtained
had the model been used in the past with what did happen. If neither prospective nor
retrospective testing is feasible, it may be possible to evaluate the solution by “sensitivity
analysis,” a measurement of the extent to which estimates used in the solution would
have to be in error before the proposed solution performs less satisfactorily than the
alternative decision procedure. The cost of implementing a solution should be subtracted
from the gain expected from applying it, thus obtaining an estimate of net improvement.
In a situation where errors or inefficiencies in applying the solution are possible, these
should also be considered in estimating the net improvement.
Fig 13.1. The four dimensions of Management
Image source: http://www.managementexchange.com/blog/what-your-management-model
If you take a good look at Fig 13.1., you will note that for each of the four dimensions, it
is possible to identify different principles by which that activity is undertaken. On the left
side, we see what might be called "traditional" principles that everyone can recognize. On
the right side, we see "alternative" principles that are less well-known but are arguably
more relevant to today’s fast-moving business environment. The 4 dimensions of
management are;
i. Choices about how activities are coordinated in the firm. Do managers focus on
using formal and well-structured management processes to deliver outputs? Or do
they encourage a process of informal and spontaneous coordination through
mutual adjustment?
ii. Choices about how decisions are made in the firm. Do managers take personal
responsibility for decision making, and rely primarily on their own deep
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knowledge and experience? Or do they prefer to tap into the disparate knowledge
of their subordinates and assign collective responsibility?
iii. Choices about the nature of the objectives the firm pursues. Do managers have a
clear set of short-term goals for the firm? Or do they pursue an oblique, or
indirect, path through the definition of a higher-level and longer-term set of
objectives?
iv. Choices about how individuals are motivated to pursue these objectives. Do
managers attempt to hire and retain good people by making extrinsic rewards,
such as salary, benefits, and bonuses attractive? Or do they focus on intrinsic
rewards such as the opportunity to contribute to society, a feeling of achievement,
or peer recognition?
In-text Question
• In testing the solution derived from a model, identify the dimensions in which
such tests could take?
o The test may be prospective, against future performance, or retrospective,
comparing solutions that would have been obtained had the model been used in
the past with what is obtained.
Box 13.3. The 4 dimensions of management are;
1. Choices about how activities are coordinated in the firm
2. Choices about how decisions are made in the firm
3. Choices about the nature of the objectives the firm pursues
4. Choices about how individuals are motivated to pursue these objectives
13.3. Model Building Process
We are still on our lecture discussing Model in Education. At this point, we are looking at
the Model Building Process.According to Bailey (1981) for the SEL at NASA Goddard
Space Flight Centre. The processes stated here are;
1. Compute the background equation
i. Picking and defining measures of size and effort
ii. Selecting the form of the base-line equation
iii. Calculating an initial base-line for use in the model
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2. Analyze the factors available to explain the difference between actual effort and
effort as predicted by the background equation
i. Choosing a set of factors (could be a large number >100)
ii. Grouping and compressing this data
iii. Isolating the important factors and groups
iv. Incorporating the factors by performing a multiple regression to predict the
deviations of the points from the computed base-line
3. Use this model to predict the effort for the new project
i. Estimate size of new project
ii. Use base-line to get standard effort
iii. Estimate necessary factor values
iv. Compute difference this project should exhibit
v. Apply that difference to standard effort
At this point, let us consider some of the management models that we have.
13.4. Lewin’s Change Management Model
This change management model was created in the 1950s by psychologist Kurt Lewin.
Lewin noted that most people tend to prefer and operate within certain zones of safety.
He recognized three stages of change. As presented in Fig 13.2., these stages are;
1. Unfreeze – Most people make an active effort to resist change. To overcome this
tendency, a period of thawing or unfreezing must be initiated through motivation.
2. Transition – Once change is initiated, the company moves into a transition period,
which may last for some time. Adequate leadership and reassurance is necessary
for the process to be successful.
3. Refreeze – After change has been accepted and successfully implemented, the
company becomes stable again, and staff refreezes as they operate under the new
guidelines.
While this change management model remains widely used today, it is takes time to
implement. Of course, since it is easy to use, most companies tend to prefer this model to
enact major changes.
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Fig 13.2. Lewin’s Change Management Model
Image source: http://2012books.lardbucket.org/books/management-principles-v1.0/s11-04-planning-and-executing-
change-.html
Box 13.4. Model Building Processes
The processes are;
1. Compute the background equation.
2. Analyze the factors available to explain the difference between actual effort and effort
as predicted by the background equation.
3. Use this model to predict the effort for the new project.
13.5. McKinsey 7-S Model
The McKinsey 7-S model offers a holistic approach to organization. This model, created
by Robert Waterman, Tom Peters, Richard Pascale, and Anthony Athos during a meeting
in 1978, has 7 factors that operate as collective agent of change as seen in Fig 13.3. These
factors are; shared values; strategy; structure; systems; style; staff and skills.
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Fig. 13.3. Mc Kinsey 7-S Model
Image source: http://www.slideshare.net/manumelwin/mc-kinsey-7s-model-strategic-implementation-manu-melwin-
joy
13.5.1. The Benefits of McKinsey 7-S Model
You need to note that this model offers the following benefits;
1. It offers an effective method to diagnose and understand an organization.
2. It provides guidance in organizational change.
3. It combines rational and emotional components.
4. All parts are integral and must be addressed in a unified manner.
13.5.2. The Disadvantages of McKinsey 7-S Model are:
1. When one part changes, all parts change, because all factors are interrelated.
2. Differences are ignored.
3. The model is complex.
4. Companies using this model have been known to have a higher incidence of failure.
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13.6. Kotter’s 8 Step Change Model
Another model we are about to consider here is Kotter’s 8 step Change Model. This
model was created by Harvard University Professor John Kotter, causes change to
become a campaign. Employees buy into the change after leaders convince them of the
urgent need for change to occur. As presented in Fig 13.4., there are 8 steps are involved
in this model.
Fig 13.4. Kotter’s 8 step change model
Image source: https://www.linkedin.com/pulse/using-kotters-8-step-organisational-
change-model-success-riche
As presented in Fig 13.4., the steps available in this model are;
1. Increase the urgency for change.
2. Build a team dedicated to change.
3. Create the vision for change.
4. Communicate the need for change.
5. Empower staff with the ability to change.
6. Create short term goals.
7. Stay persistent.
8. Make the change permanent.
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Activity 13.1.
Take a good look at the different models discussed during this lecture and make a
schematic representation of each of these models on a cardboard paper showing how the
different steps interact.
Activity 13.1. Feedback
Your sketch should clearly indicate the different steps involved in each model.
13.6.1. Advantages of Kotter’s 8 Step Change Model
Significant advantages to the model are:
1. The process is an easy step-by-step model.
2. The focus is on preparing and accepting change, not the actual change.
3. Transition is easier with this model.
13.6.2. Disadvantages of Kotter’s 8 Step Change Model
There are some disadvantages offered by this model. These are;
1. Steps can’t be skipped.
2. The process takes a great deal of time.
It doesn’t matter if the proposed changed is a change in the process of project planning or
general operations. Adjusting to change is difficult for an organization and its employees.
Using almost any model is helpful, because it offers leaders a guideline to follow, along
with the ability to determine expected results. This is helpful because change is difficult
to implement and manage.
Summary of Session 13
In this lecture, you have learned that;
1. A model is a simplified representation of the real world and as such includes only
those variables relevant to the problem at hand.
2. There are four patterns of model construction, only two of which involve
experimentation: inspection, use of analogues, operational analysis, and
operational experiments.
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3. Models not only assist in solving problems but also are useful in formulating
them; that is, models can be used as guides to explore the structure of a problem
and to reveal choices that might otherwise be missed.
4. Procedures for deriving solutions from models are either deductive or inductive.
5. A model may be deficient because it includes irrelevant variables, excludes
relevant variables, contains inaccurately evaluated variables, is incorrectly
structured, or contains incorrectly formulated constraints.
6. The solution derived from a model is tested to find whether it yields better
performance than some alternative, usually the one in current use. The test may be
prospective, against future performance, or retrospective, comparing solutions that
would have been obtained had the model been used in the past with what is
obtainable.
7. A Management Model is simply the set of choices made by executives about how
the work of management gets done about how they define objectives, motivate
effort, coordinate activities, and allocate resources.
8. The four dimensions of management:
• Choices about how activities are coordinated in the firm.
• Choices about how decisions are made in the firm.
• Choices about the nature of the objectives the firm pursues.
• Choices about how individuals are motivated to pursue these objectives.
9. The Model Building Processes are:
• Compute the background equation
• Analyze the factors available to explain the difference between actual effort
and effort as predicted by the background equation
• Use this model to predict the effort for the new project
10. Some of the management models we have are; Lewin's Change Management
Model; Mckinsey 7sModel; Kotter's 8 step change model etc.
Self-Assessment Questions (SAQs) for Session 13
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
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SAQ 13.1. (tests learning outcome 13.1.)
In the statements provided here, fill the blanks with the most appropriate keywords
a. A _______is a simplified representation of the real world and includes only those
variables relevant to the problem at hand.
b. The choices made by organisation’s top executives regarding how they define
objectives, motivate effort, coordinate activities and allocate resources can be best
described as _________.
c. _________ model is used to describe a system that has the same structure as another
but may be different in content and can be used as a model of the other.
d. _________and ________ models are frequently used in the preliminary phases of
constructing symbolic models of systems.
e. With _______ one moves directly from the model to a solution in either symbolic or
numerical form.
f. __________ procedures involve trying and comparing different values of the
controlled variables.
SAQ 13.2. (tests learning outcome 13.2.)
Using the knowledge gained in this lecture, how would you describe a model in a
managerial context?
SAQ 13.3. (tests learning outcome 13.3.)
One of the chief functions of a model is to derive solution to a problem. In doing this,
what are the procedures involved?
SAQ 13.4. (tests learning outcome 13.4.)
As a manager, model building is a task that is needed to improve productivity in the
organization. To achieve this, how can a model be built?
SAQ 13.5. (tests learning outcome 13.5.)
Based on what you have learnt in this lecture, identify some of the models treated and
state the steps involved.
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References
Sutton, C.D. (2005). Classification and Regression Trees, Bagging, and Boosting, in
Handbook of Statistics, Vol. 24, pp. 303-329, Elsevier.
Quinlan, J. R. 2006. Bagging, Boosting, and C4.5. In AAAI 96: Proceedings of the 13th
National. Conference on Artificial Intelligence (Vol. 2, pp. 725–730).
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Study SessionFourteen: Decision Making Process: PPBS
Expected duration: 2 weeks or 4 contact hours
Introduction
Welcome back to the 14th lecture on EME 302. At this stage, it should not be strange to
you that managers at all organizational levels make decisions although they differ in
terms of type and scope. At the top level of the organization, decisions establishing
overall objectives and strategies are among the most important to be made. Middle level
managers are generally more involved with decisions involving overall operating policies
and plans. First line supervisors in turn, are concerned with short range decisions that
relate to specific activities to be carried out within the framework of policies and plans,
established at middle management levels. In this lecture, you will get to learn more from
the decision-making process in Planning, Programming, Budgeting system.
Learning Outcomes for Study Session 14
At the end of this lecture, it is expected that you will be able to;
14.1. Define and use correctly keywords printed in bold. (SAQ 14.1.)
14.2. Explain what Decision-Making entails. (SAQ 14.2)
14.3. Distinguish clearly between types of decisions. (SAQ 14.3)
14.4. State the procedure of PPBS to organisation’s decision making process.
(SAQ 14.4)
14.5. Outline at least 5 techniques used in decision-making. (SAQ 14.5)
Key words; decision-making, decision-making process, programmed decisions, non-
programmed decisions, and groups.
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14.1. Meaning of Decision Making and Types of Decisions
14.1.1. Meaning of Decision Making
Decision making is so basic that no management function can be performed without it.
For management purposes, decisions are obviously required in planning, organization,
actuating, and controlling.Decision making is the cornerstone of planning because it is
the catalyst that drives the planning process. An organization’s goals follow from
decisions made by various managers. Furthermore, in deciding to adopt the best plan for
achieving goals, decision making basically reflects the selection of the best choice among
possible alternatives and putting it into practice. Effective decision making requires that
the decision maker understands the situation driving the decision. However, it can be
argued that management is simply decision making and that the essence of managerial
behaviour is found by studying decision making. In addition, decision making often
reflects the manager’s effort to make sense of the complicated environment, to attain
some control over the uncontrollable and to achieve some sense of order. Finally, when
an organized approach to decision making is employed, such as having a clear
understanding of the present state of affairs, historical basis for improving decisions, and
the possible errors that can be made, it enables managers to make better decisions and to
reach personal and organizational goals.
Decision making is a continuous process that pervades all organizational activities.
Managers in every type of organization; business; hospital; government and education
make decisions every day. To this extent, understanding what makes an organization
successful depends upon our knowledge of how people make effective decisions. A
decision is defined as a conscious choice among alternative courses of action followed by
activities to implement the choice. Thus, we must recognize that managerial decision
making entails both a process and subsequent action. A decision-making process is a
series or chain of related steps that lead up to an action or an outcome and assessment.
Ivancevich, et al, (1994) explain that decision making can be understood as a series of
steps that run from clearly identifying a problem to implementing and assessing actions.
Using such a systematic approach to decision making ensures that relevant information
has been gathered, alternative choices have been considered, and possible consequences
of actions understood.
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Box 14.1. Decision Making
Note that;
• Effective decision making requires that the decision maker understands the situation
driving the decision. It can be argued that management is simply decision making and
that the essence of managerial behaviour is found by studying decision making.
• A decision-making process is a series or chain of related steps that lead up to an action
or an outcome and assessment.
14.1.2. Types of Decisions
There are basically 2 types of decisions, these are; Programmed and Non-Programmed
Decisions.
1. Programmed Decisions – if a situation occurs often and in the same form, a
routine procedure usually will be worked out for dealing with it. Decisions are
programmed to the extent that they are repetitive and routine. Examples are: the
procedure for opening a bank account; reorder of inexpensive materials; procedure
for admitting patients in hospitals.
2. Non-programmed Decisions – decisions are non-programmed when the problem
is unstructured.
14.2. Planning, Programming, Budgeting System (PPBS)
We have come to another phase in this lecture where we shall examine the PPBS
technique. Output budgeting wide ranging management technique introduced into the
USA in the mid-1960s, not always with ready cooperation with the administrators and
based on the industrial management techniques of program budgeting. Subsequently, the
technique has been introduced into other countries, including the UK where it is often
called output budgeting. PPBS is in effect on integrating of several techniques in a
planning and budgeting process for identifying, costing and assigning a complexity of
resources for establishing priorities and strategies in a major program and for forecasting
costs, expenditure and achievements within the immediate financial year or over a longer
period.Some of the procedures of PPBS are discussed afterwards.
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14.2.1. Decision-Making under states of Certainty, Uncertainty and Risk
It is essential for you to know that decision-making can fall under 3 states as it will be
discussed below. We have;
1. Decision making certainty:When decision maker knows with certainty the
probabilities of the outcomes of each alternative and what conditions are
associated with each alternative, the decision is said to be under certainty. An
example of this type of decision is a decision to purchase items from a supplier
that regularly supplies the items.
2. Decisions making under uncertainty: When the decisions maker has absolutely
no knowledge of the probabilities of the outcomes of each alternative, the risks
associated with each, or the consequences each alternative is likely to have.
3. Decisions making under risk: When the decisions maker has some probabilistic
estimate of the outcomes of each alternative.
In-text Question
• Based on what you have learnt, how would you describe around procedures such
as the procedure for opening a bank account; reorder of inexpensive materials;
procedure for admitting patients in hospitals.
o These are called programmed decisions.
14.2.2. Proactive and Reactive Decisions
Another point you need to know under PPBS is that decisions can be viewed from 2
perspectives such as;
1. Proactive Decisions: A decision made in anticipation of a change in the external
environment or other condition is called a proactive decision. Managers who
utilize a systematic, proactive approach anticipate problems and seek to prevent
them from occurring or minimizing their impact on operations.
2. Reactive Decisions: A reactive decisions is one made in response to external
changes that have already taken place. When a manager initiates action to correct
product defects because of persistent customer complaints, he or she adopting a
reactive approach to making decisions. Rather than apply preventive maintenance
(proactive), a machine shop manager may spend money only to repair broken
down machines (reactive).
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14.2.3. The Rational Decision Making Process
As the heading implies, for a decision to be tagged rational, it must pass through the
following processes as seen in Fig 14.1.
Fig 14.1. Rational Decision Making Process
Image source: https://www.24point0.com/example-decision-making-template/
Step 1: Diagnose and Define Problem or Opportunities: The origin of a problem is not
always obvious. If managers are to remedy a situation, they must first find out what the
real problem is. One way to do this is to ask what past action or lack of action might have
caused this situation to arise? In this way, managers can focus upon the events or
circumstances that most likely led to the problem. An opportunity is a gap, an unsatisfied
need or a need that is being inadequately satisfied by existing competitors and which can
be profitably exploited. As part of the process of defining the problem, managers should
also begin to determine which problems they should or would like to solve. Managers
therefore need to distinguish between their “musts” and their “should” so that they will
have a basis for proposing and evaluating solutions. That is, managers prioritize problems
to determine the ones that must be attended to and those that should be attended to.
Step 2: Establish specific Goals and Objectives: It is crucial to note that decisions
making is always done in the context of goals and objectives; and that all behaviour is
basically goal oriented. If goals and objectives are adequately established, they will
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dictate what results must be achieved and the measure that indicate whether they have
been achieved. Such measure is also referred to as the decision criteria.
Step 3: Generate Alternatives: No major decisions can be made until several possible
solutions have been generated. Otherwise, managers may be tempted to adopt the first
and most obvious solution they find. The first solution may not always be the correct one.
The manager needs to list all possible alternatives to solving the problem.
Step 4: Gather and Analyse the Relevant Facts: Once the possible alternatives have
been generated, the next logical step is to gather data suggested by each alternative. Data
may be collected from internal sources – records available in the company or external
sources. Analysis of data consists of combining or arranging the data in a firm as to
provide meaning or insight into the problem at hand. What resources will be available to
help us solve the problem? Managers will rarely get all the answers they need to such
questions. At some point, however, they should have enough information to be able to
formulate possible solutions.
Step 5: Evaluate the Alternatives: Once managers have developed a set of alternatives,
they must evaluate them to see how effective each alternative will be in solving the
problem. Effectiveness is determined based on the decision criteria identified in Step 2.
Based on the information available, the questions to be asked are: (i) how realistic the
alternative is in terms of the goals and resources of the organization, and (ii) how well
will the alternative help solve the problem. The alternatives must also be evaluated in
terms of how well they would solve the “must” and “should” of the problem. Thereafter
the alternatives are arranged in a hierarchy, which is from most desirable to least
desirable.
Step 6: Select an Alternative: At this stage, the manager chooses the best alternative
based on the decision criteria earlier established. The alternative selected is the one that is
most desirable of all the alternatives evaluated.
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Step 7: Analyse the Possible Consequences of the Decision: Once managers have
selected their best alternative, they must try to anticipate what problems will occur when
implementing the decision. For example, there is often great resistance in organizations to
change.There may be practical problems involved in implementing the decision, such as
the need to obtain additional funding. Other departments in the organization that might be
affected by the decision must be consulted. Competitors may be affected by the decision,
and their reactions should be considered. Usually, however, analyzing the possible
consequences of their action will simply allow managers to take the necessary steps to
deal with them.
Step 8: Implement the Decision: Ultimately, no decision is better than the action taken to
make it a reality. If the decision is a good one, but subordinates are not willing or able to
carry it out, then it is unlikely the decision will be very effective. A frequent error of
managers is to assume that once they decide, action on it will automatically follow. Since
in most situations, implementing decisions involves people, the test of decision
soundness is the behaviour of the people who put it into action or are affected by it,
Subordinates cannot be manipulated in the same manner as other resources. Effectively
communicating with the appropriate individuals and groups and groups will ensure
success.
Step 9: Follow Up: Effective management involves periodic measurement of results.
Actual results are compared with planned results (the objective). If deviation exists,
changes must be made. Here again, we see the importance of measurable objectives. If
actual results do not meet planned results, changes must be made in the solution chosen,
in its implementation, or in the original objective if it is deemed unattainable. If the
original objective must be revised, then the entire decision making process will be
reactivated.
14.2.4. Individual Decision Making
A key function of managers is decision making. Many decisions in the organization are
made by managers as individuals. This is often the case when the decisions are routine or
programmed decisions. When the risk involved in the decision is low, managers also tend
to make such decisions as individuals. When managers select a course of action to solve a
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given problem or to take advantage of an opportunity all by himself/herself, it is known
as individual decision making. The manager may obtain information from colleagues but
the choice is made by him/ her. Examples of individual decision making are: allocation of
work to subordinates, decision to reorder raw materials from a known or regular supplier,
handling customer complaints, decision on how much discount to give a customer, etc.
The Advantages of Individual Decision making include:
a. Decision is fast.
b. Responsibility for the decision can be assigned to the person that made the
decision.
c. Implementation of the decision will be fast.
d. Job satisfaction of the manager will be high.
e. The manager’s experience is brought to bear on the decision.
Some of the disadvantages of individual decision making include:
a. The outcomes of individual decision may not be satisfactory because the decision
is likely to be influenced by individual perceptions, values and priorities.
b. The decision maker can only rely on a limited amount of information to make the
decision.
c. There might be a tendency for the manager to “pass the buck”.
d. Individual decision making is often not appropriate when the problem is complex,
novel or when the level of uncertainty is high.
14.2.5. A Group Decision-Making
A group can be defined as two or more freely interacting individuals who share a
common identity and purpose. Firstly, a group must be made up of two or more people if
it is to be considered a social unit. Secondly the individuals must share something in
common. Fourth, interacting individuals must also have a common purpose. That is, there
must be at least a rough consensus on why the group exists (Kreitner, 2000). In today’s
world, a great deal of decision making is achieved through groups. These interacting
groups and teams are the most common form of decision making groups with such names
committees, teams, boards, task forces, etc. This tendency toward group decision making
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is due in part to organizations‟ increased complexity and the large amount of information
needed to make sound decisions.
Many favour group decision making, believing it gives those who will be affected by a
decision a chance to participate in it and helps to develop the members of the group.
Furthermore, the advocates of group decision making state that in this age of
technological change, government influence, and social responsibility, the issues to be
decided have grown beyond the expertise of a single manager. The input of many people
is called for since each is unique in knowledge and experience. The sharing of decision
making responsibilities establishes inter-dependence among the parties. Thus, group
cooperation is enhanced and the old authoritarian concept of decision making is reduced.
Group decision making would become particularly appropriate for non-programmed
decisions because these decisions are complex and few individuals have all the
knowledge and skills necessary to make the best decisions. Thus, group decision making
becomes invaluable when they can maximize the unique contribution of everyone.
Advantages of Group Decision-Making
In general, it is expected that a group would tend to make more effective decisions than
would any single individual. Some of the advantages of group decision making are
summarized below:
a. Since the group members have different specialties, they tend to provide more
information and tend to be more comprehensive in nature.
b. The group can generate a greater number of alternatives.
c. Implementation of the decisions is more effective, since the people who are going
to implement the decision also participated in the decision process. This increases
the commitment of the people to see to the implementation for success.
d. The input from many people eliminates the biases that are generally introduced in
individual decision making. It also reduces the unreliability of individual’s
decisions.
e. The participative decision making process builds up a training ground for
subordinates who develop the skills of objective analysis, evaluation and decision
making.
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f. Group decision making is more democratic in nature while the individual decision
making is more autocratic in nature. The democratic processes are more easily
acceptable and are consistent with the democratic ideals of our society.
Disadvantages of Group Decision-Making
There are certain drawbacks to group decisions also. Some disadvantages are:
a. It is time-consuming. It takes a great deal of time to assemble the group. In
addition, a group takes more time in reaching a decision since there are many
opinions to be taken into consideration.
b. Some members may simply agree with the others for the sake of agreement since
there are social pressures to conform and not to be the odd person.
c. There may be some personality conflicts that may create inter-personal obstacles
which may diminish the efficiency of the process as well as the quality of the
decision.
d. The decision made by the group may not always be in accord with the goals and
objectives of the organization. This is especially true when the goals of the group
conflict with those of the organization.
e. The group members may exhibit “focus effect.” This means that the group may
focus on one or a few suggested alternatives and spend all the time evaluating
these and may never come up with other ideas, thus limiting the choices.
Box 14.2. The procedures in PPBS are;
1. Decision-Making under states of Certainty, Uncertainty and Risk
2. Proactive and Reactive Decisions
3. The Rational Decision Making Process
4. Individual Decision Making
5. A Group Decision-Making
14.3. Decision Making Techniques
We have come to another point in this lecture where we shall be considering decision
making techniques. Decision making techniques can be defined as tools that managers
can use to enhance the efficiency and effectiveness of decision making. There are
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different techniques discussed in this section that are used at different stages of the
decision-making process. These techniques consist of an orderly, systematic framework
for defining, analyzing and solving problems in an objective and scientific manner. They
are intended to improve the manager’s decision making ability and provide them with a
means for justifying and evaluating their own managerial performance. Some of these
techniques are discussed below;
14.3.1. Brainstorming
In many situations, groups are expected to produce imaginative solutions to
organizational problems. In such instances, brainstorming has often enhanced the group’s
creative output. Brainstorming is a process where a group of individuals generate ideas
according to a firm set of rules designed to promote the generation of new ideas while at
the same time avoiding members‟ inhibitions that face-to-face groups usually cause. The
basic rules are: (a) No idea is too ridiculous. Group members are encouraged to state any
extreme or outlandish ideas that occur to them. (b) Each idea presented belongs to the
group, not the person stating it. In this way, group members utilize and build on the ideas
of others. (c) No idea can be criticized. The session’s purpose is to generate ideas, not to
evaluate them.
14.3.2. The Delphi Technique
The Delphi technique is a systematic procedure sometimes used for developing a
consensus among a group of experts. Here, the experts are given a series of detailed
questionnaires about a problem and then are asked to provide their own written opinions.
The use of questionnaires avoids direct contact and debate among experts, which might
induce hasty formulation and commitment to certain ideas. After reading the anonymous
answers of other participants, each expert revises his or her own answers. Eventually,
after a series of “rounds” of this type, convergence of opinion usually occurs. (Stoner,
1978:208). When the opinions stabilize, the average opinion is taken to represent the
decision of the “group” of experts. (Griffin, 1999:281) The underlying belief is that the
consensus estimate results in a better decision after several rounds of anonymous group
judgement. While it is possible to continue the procedure for several rounds, research has
shown that, typically, no significant changes occur after the second round of feedback.
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14.3.3. The Nominal Group Technique (NGT)
NGT is a process of bringing people together as a group to solve a problem. NGT
combines both verbal and non-verbal stages. Basically, NGT is a structured group
meeting that proceeds as follows:
a. A group of 7 to 10 individuals sit around a table but do not speak to one another.
Talking to each other is not permitted during the first stage of NGT. Rather, each
person writes ideas on a note pad about the problem to be solved.
b. After five minutes, a structured sharing of ideas takes place. Each person presents
one idea. A person designated as recorder writes the ideas down on a flip chart in
full view of the entire group. This continues until all the participants indicate that
they have no further ideas to share. There is still no discussion.
c. The output of this phase is usually a list of 18 to 25 ideas. The next phase involves
structured discussion in which each idea receives attention before a vote is taken.
d. In the next stage, independent voting, each participant privately selects priorities
by ranking or voting. The group decision is the mathematically pooled outcome of
the individual votes. Both the Delphi technique and NGT have excellent records of
successes. There are two basic differences between them:
i. In the Delphi process, all communication between participants is by way of
written questionnaires and feedback from monitoring staff. In NGT,
communication is direct between participants.
ii. NGT participants meet face-to-face around a table, while Delphi participants are
physically distant, never meet face-to-face, and are typically anonymous to one
another. Practical considerations, of course, often influence which technique is
used. These considerations can include:
� the number of working hours available
� costs, and
� participants‟ physical proximity.
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14.3.4. Marginal Analysis
Marginal analysis is a technique that can be used to evaluate alternatives by comparing
the additional revenues and additional costs as output increases. The technique is useful
where the objective is to maximize profit, or to find the best output of a typical
educational institution. The idea of marginal analysis is based on the simple economic
postulation that profit is maximized where marginal revenue (additional revenue) is equal
to marginal cost (additional cost). Hence in evaluating alternatives, the decision maker
seeks to find the point where the additional revenue is equal to the additional cost or the
point where the value of additional input is equal to the value of additional output.
14.3.5. Cost Benefit or Cost Effectiveness Analysis
Cost Benefit Analysis is an improvement on marginal analysis. It enables the decision
maker to compare the ratio of costs to benefits of alternative courses of action and to
select the alternative that has the best ratio. The best ratio is that which yields the least
costly means of achieving an objective or the expenditure that yields the greatest value.
14.3.6. Decision Trees
One of the best ways to analyze a decision is to use the so-called decision tree. Decision
trees depict, in the form of a “tree,” the decision points, chance events and probabilities
involved in various courses that might be undertaken as described in the example
presented on Fig 14.2.
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Fig 14.1. An image showing an example of a decision-making tree
Image source: https://www.edrawsoft.com/decisiontreeexamples.php
We can also define a decision tree as a graphical method of displaying various parts of
the decision-making process including courses of action, risks involved and likely
outcomes. It enables the decision makers to consider alternative solutions, assign
financial values to them, estimate the probability of a given outcome for each alternative,
make comparisons and choose the best alternative. A common problem occurs in
business when a new product is introduced. The manager must decide, among various
options, whether to: (a) Install expensive permanent equipment and ensure production at
the lowest possible cost or (b) Undertake cheaper technology tooling that will involve a
higher manufacturing cost but lower capital investments that will result in smaller losses
if the product does not sell as estimated.
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Box 14.3. Decision-Making Techniques
Some of the decision-making techniques are;
1. Brainstorming
2. The Delphi Technique
3. The Nominal Group Technique (NGT)
4. Marginal Analysis
5. Cost benefit or cost effectiveness analysis.
Activity 14.1.
You have been faced with a demand to decide on the best way to pass your examinations
either by studying at intervals or waiting for the release of examination timetable before
commencing study. Using the decision tree, get a broadsheet of paper and analyse why
you need to decide on the option you are going for.
Activity 14.1. Feedback
On your decision tree, passing your examination should be the primary decision which
will be linked to your evaluation of the approaches and methods you are deploying in
arriving at that decision.
Summary of Unit 14
In this lecture, you have learned that;
1. Decision making is the selection of a course of action from among alternatives; it
is the core of planning. Managers make decisions that must be carried out by
others. The type of decisions they make, and the conditions under which they
make them, will vary. They must therefore tailor their decision-making approach
to their problems and circumstances.
2. Programmed decisions are those that are suggested by habit or policy. Non-
programmed decisions are those that are new.
3. Decision-making can fall under 3 states such as certainty, uncertainty, and risks.
4. Most important decisions will be non-programmed: they will require careful and
logical consideration.They involve nine stages: (i) diagnose and define the
problem (ii) Establishing specific goals and objectives (iii) generate alternatives
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(iv) gather and analyse the facts (v) evaluate alternatives (vi) select best alternative
(vii) analyse possible consequences (viii) Implement decision, and (ix) follow up.
Finally, various management techniques in decision making were highlighted.
5. Many decisions in the organization are made by managers as individuals. This is
often the case when the decisions are routine or programmed decisions.
6. Some of the decision-making techniques we have are; brainstorming; Delphi
technique; norminal group technique; marginal analysis; cost benefit or cost
effective analysis and decision trees.
Self-Assessment Questions (SAQs) for Session 14
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 14.1. (tests learning outcome 14.1.)
In the statements provided here, fill the blanks with the most appropriate keywords
a. ________ is the cornerstone of planning because it is the catalyst that drives the
planning process.
b. If a situation occurs often and in the same form, a routine procedure usually worked
out for dealing with such can be termed __________.
c. Decisions are __________ when the problem is unstructured.
d. A ________ can be defined as two or more freely interacting individuals who share
a common identity and purpose.
e. A _________ is a series or chain of related steps that lead up to an action or an
outcome and assessment.
SAQ 14.2. (tests learning outcome 14.2.)
Decision making is vital in an organization as it can either make or mar an
organizationalgoal. On this note, shed more light on decision making.
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SAQ 14.3. (tests learning outcome 14.3.)
Considering these 2 scenarios, identify the types of decisions present in both
1. How you manage blackout at your hostel whenever there is a need for you to study.
2. Changing your course of study based on your inability to meet your current course
requirements.
SAQ 14.4. (tests learning outcome 14.4.)
In describing PPBS to organisation’s decision making process, what are the procedures
involved?
SAQ 14.5. (tests learning outcome 14.5.)
During this lecture, it was mentioned that managers can use certain tools to enhance the
efficiency and effectiveness of decision making.Outline some of these tools.
References
Doh, J. C. 1971. The planning-programming-budgeting systems in three federal agencies.
Manchester, NH: Irvington.
Grimes, S. R. Carlisle, P. A. 2008; “PPBS to PPBE: A Process or Principles?” U.S. Army
War College.
Wade P. H., Milton L. T., Gordon C. V., Rachel D. D, 2010; Planning, Programming, and
Budgeting System (PPBS)/Multi-year Programming, Institute for Defense
analysis; Reading Guide, IDA Document D-4057, Log: H 10-000982
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Study Session Fifteen: Management by Objectives (MBO)
Expected duration: 1 week or 2 contact hours
Introduction
As we approach the end of this course, this lecture is geared towards exposing you to the
topic; management by objectives. The principle behind Management by Objectives
(MBO) is to make sure that everybody within the organization has a clear understanding
of the aims, or objectives, of that organization, as well as awareness of their own roles
and responsibilities in achieving those aims. Employee empowerment is allowing
workers to make decisions that would otherwise come from management. By
empowering employees who have direct knowledge about the matter at hand, services are
delivered efficiently. Also, a decentralized decision-making process is cost-effective
because it streamlines the firm by getting rid of excess manpower, mainly in the middle
management.
Learning Outcomes for Study Session 15
At the end of this lecture, it is expected that you will be able to;
15.1. Define and use correctly keywords printed in bold. (SAQ 15.1.)
15.2. State MBO in relation to the organisation’s mission, vision and objectives.
(SAQ 15.2)
15.3. Identify the trends in which MBO works in an organization. (SAQ 15.3)
15.4. Enumerate the elements of MBO according to Peter Drucker.(SAQ 15.4)
Key words; goal-setting, planning, top-down process, and bottom-up process.
15.1. Meaning, Strengths and Weaknesses of Management by Objectives
15.1.1. Meaning of Management by Objectives
Management by Objectives is a technique used by management to achieve collaboration
between managers and their subordinates in goal-setting and planning processes. The
approach was first proposed by Peter Drucker in his 1954 book “The Practice of
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Managemen”. Since that time, MBO has spurred a great deal of discussions, evaluation,
research, and inspired many similar programmes. The features of this concept are:
i. It refers to a formal set of procedures that begins with goal setting and continues
through performance review.
ii. Managers and those they supervise act together to set common goals.
iii. Each person’s major areas of responsibility are clearly defined in terms of
measurable expected results or objectives. These are used by subordinates in
planning their work.
iv. At periodic intervals, the expected results or objectives jointly set by managers and
their subordinates are used to monitor and review progress.
v. Based on the agreed objectives or results, the performance of subordinates is
evaluated.
A management system is in which the objectives of an organization are agreed upon so
that management and employees understand a common way forward. Management by
objectives aims to serve as a basis for the following; You can pause to consider these
bases.
• greater efficiency through systematic procedures,
• greater employee motivation and commitment through participation in the
planning process, and
• planning for results instead of planning just for work. In management by
objectives practice, specific objectives are determined jointly by managers and
their subordinates, progress toward agreed-upon objectives is periodically
reviewed, end results are evaluated, and rewards are allocated based on the
progress.
In-text Question
• What basic function do you think management by objectives strives to achieve in
an organization?
o It is used to achieve collaboration between managers and their subordinates in
goal-setting and planning processes.
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In addition, Management by objective (MBO) is a process through which specific goals
are set collaboratively for the organization and every unit and individual within it; the
goals then are used as a basic for planning, managing organizational activities, and
assessing and rewarding contributions. In Management by objectives (MBO) specific
performance goals are jointly determined by employees and their managers. Progress
towards accomplishing these goals is periodically reviewed, and rewards are
allocatedbased on this progress. Peter Drucker stated that Management by Objectives
consists of four elements which are;
i. Goal specificity
ii. Participative decision making
iii. Explicit time-period
iv. Performance feedback
MBO makes objectives operational through the process by which they cascade down
through the organization. Although there is considerable variation across organizations.
MBO processes typically include five steps which are;
1. Organizational goals are developed based on organizational missions.
2. Specific goals are established for departments, subunits, and individuals.
• In the top-down process, upper-level managers, conferring with their
immediate managerial subordinates, formulate specific objectives for their
areas of responsibility. These in turn enter the formulation of objectives for the
next level down, and so forth.
• In the bottom-up process, operational goals are proposed by lower-level
managers based on what they think they can achieve. These in turn are
developed into tactical and finally strategic plans.
3. Action plans are formulated, describing what is to be done, how, when, where,
andby whom to achieve a goal.
4. Individuals are given the responsibility of reaching their objectives and that
goalswill ultimately be met.
5. Performance is appraised at the end of the goal-setting cycle, typically at one-
yearintervals. Praise, recognition, and rewards should be given for effective
performance.
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Box 15.1. The Elements of Management by Objectives according to Peter Druker
are;
1. Goal specificity
2. Participative decision making
3. Explicit time-period
4. Performance feedback
As we proceed in this lecture, let us consider the strengths of Management by Objectives
(MBO).
15.1.2. Strengths of Management by Objectives
These are;
1. Aids coordination of goals and plans.
2. Helps clarify priorities and expectations.
3. Facilitates vertical and horizontal communications.
4. Fosters employee motivation.
15.1.3. Weaknesses of Management by Objectives
The weaknesses of MBO are that it;
1. Tends to falter without strong, continual commitment from top management.
2. Necessitates considerable training of managers.
3. Can be misused as a punitive device.
4. May cause overemphasis of quantitative goals.
The "spirit" of MBO is tremendous. In practice,MBO has been successful only about 20
to 25 percent of the time, primarily because of lack of support from top management and
poor goal-setting and communication skills. For MBO to be successful, the objectives
must meet five criteria. They must be;
1. arranged in order of their importance;
2. expressed quantitatively, wherever possible;
3. realistic;
4. consistent with the organization's policies, and;
5. compatible with one another.
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Suggested by the management guru Peter Drucker (1909-2005) in early 1950s,
management by objectives enjoyed huge popularity for some time but soon fell out of
favor due to its rigidity and administrative burden. Its emphasis on setting clear goals,
however, has been vindicated and remains valid.
15.2. Activities in Management by Objectives (MBO)
Some of the activities in management by objectives are;
1. Time Span of Goals and Plans
• Strategic goals and plans generally involve time periods of 3-5 years.
• Tactical goals and plans typically involve time periods of 1 to 3 years.
• Operational goals and plans can be for as short a period as 1 week or as long as
1 year.
Characteristics of Well-Designed Goals are;
a. Written in terms of outcomes
b. Measurable and quantifiable
b. Clear as to a time frame
c. Challenging but attainable
d. Written down
e. Communicated to all organizational members
So, if I may ask you, what are the Steps in Goals Setting? These steps are stated below;
a. Review the organization's mission. Goals should reflect what the mission statement says.
b. Evaluate available resources.
c. Determine individually, or with input from others, the goals.
d. Write down the goals and communicate them to all who need to know.
e. Review results and whether goals are being met.
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2. Developing Plans
The process of developing plans is influenced by three contingency factors and by the
planning approach are;
a. Manager's level in the organization: Operational planning usually dominates the
planning activities of lower-level managers. As managers move up through the
levels of the organization, their planning becomes more strategic.
b. Degree of environmental uncertainty: The greater the environmental uncertainty,
the more plans should be directional and emphasis placed on the short term.When
uncertainty is high, plans should be specific, but flexible.Managers must be
prepared to rework and amend plans, or even to abandon their plans.
c. Length of Future Commitments: Commitment concept means that plans should
extend far enough to meet those commitments made when the plans were
developed.Planning for too long or for too short a period is inefficient and
ineffective.
Before rounding up this lecture, let us examine this;
Approaches to Establishing Goals
Goals can be established through a process of traditional goal setting or through MBO.
Traditional goal setting is defined as the process whereby goals are set at the top of
theorganization and then broken down into sub goals for each level in an organization. In
this process;
1. Top managers are assumed to know what's best because they see the "big picture."
2. These goals are also often largely non-operational.
3. Specificity is achieved as each manager applies his or her own set of
interpretations and biases.
4. However, what often results are that objectives lose clarity and unity as they move
from top to bottom.
5. When the hierarchy of objectives is clearly defined, it forms an integrated means-
end chain in which higher-level objectives are linked to lower-level objectives.
These lower-level objectives serve as the means for the accomplishment of the
higher-level objectives. And the goals at the lower levels (means) must be
achieved to reach the goals at the next level ends.)
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In the same vein, do you know that goals setting has some pitfalls.? These would be
discussed shortly
Potential pitfalls in Goals Setting
These are;
1. Setting difficult goals increases the risk that they will not be reached.
2. High goals may increase the stress levels of organizational members.
3. Failure to meet high goals may undermine the self-confidence of organizational
members.
4. Non-goal areas may be ignored.
5. Setting goals may encourage excessive shot-range thinking.
6. Inappropriate goals may lead to dishonesty and cheating.
Summary of Session 15
In this lecture, you have learned that;
1. MBO is an effective technique for integrating goal setting and planning. This
process of MBO essentially involves managers and subordinates meeting to
establish specific objectives and periodically reviewing progress toward those
objectives.
2. A management system is in which the objectives of an organization are agreed
upon so that management and employees understand a common way forward.
3. Peter Drucker stated that Management by Objectives consists of four elements
which are; goal specificity; participative decision making; explicit time-period;
and performance feedback.
4. MBO makes objectives operational through the process by which they cascade
down through the organization.
5. The strengths of MBO are that it aids coordination of goals and plans, helps clarify
priorities and expectations, facilitates vertical and horizontal communications and
fosters employee motivation.
6. The weaknesses of MBO are that it; tends to falter without strong, continual
commitment from top management; necessitates considerable training of
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managers; can be misused as a punitive device and may cause overemphasis of
quantitative goals.
7. For MBO to be successful, the objectives must meet five criteria. They must be;
arranged in order of their importance; expressed quantitatively wherever possible;
realistic; consistent with the organization's policies, and; compatible with one
another.
8. Some potential pitfalls in goals setting are; setting difficult goals increases the risk
that they will not be reached; high goals may increase the stress levels of
organizational members; failure to meet high goals may undermine the self-
confidence of organizational members; non-goal areas may be ignored etc.
Self-Assessment Questions (SAQs) for Session 15
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 15.1. (tests learning outcome 15.1.)
In the statements provided here, fill the blanks with the most appropriate keywords
a. Management by Objectives is a technique used by management to achieve
collaboration between managers and their subordinates in _________ and
_________ processes.
b. In the ___________, upper-level managers, conferring with their immediate
managerial subordinates, formulate specific objectives for their areas of
responsibility.
c. In the __________, operational goals are proposed by lower-level managers based
on what they think they can achieve.
SAQ 15.2. (tests learning outcome 15.2.)
In describing Management by Objectives (MBO), how does it relates with organisation’s
mission, vision and objectives?
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SAQ 15.3. (tests learning outcome 15.3.)
You learnt in this lecture that MBO makes objectives operational through the process by
which they cascade down through the organization. Describe this process.
SAQ 15.4. (tests learning outcome 15.4.)
Peter Drucker stated that Management by Objectives consists of four elements. Identify
these elements.
References
Antoni, C. 2005, Management by objectives – an effective tool for teamwork?
International Journal of Human Resource Management, Vol. 16.
Hollenbeck, J.R. and Klein, H.J. 1987 ‘Goal Commitment and the Goal Setting Process:
Problems, Prospects, and Proposals for Future Research’, Journal of Applied
Psychology.
Locke, E.A. and Latham, G.P. 1990, A Theory of Goal Setting and Performance,
Englewood Cliffs, NJ: Prentice Hall.
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Study Session Sixteen: Linear Programming
Expected duration: 1 week or 2 contact hours
Introduction
I’m welcoming you on board to the last lecture in EME 302 (Operations Management in
Educational Practice). I want to believe that you have gained the needed skills that was
stated in the objectives of this course. To round up the lectures in this course, this lecture
will be discussing Linear Programming. This is a mathematical technique for determining
the optimal allocation of the resources and obtaining an objective when there are
alternative uses of resources. This lecture examines the model in application to education.
Learning Outcomes for Study Session 16
At the end of this lecture, it is expected that you will be able to;
16.1. Define and use correctly keywords printed in bold. (SAQ 16.1.)
16.2. Explain the meaning of Linear Programing. (SAQ 16.1)
16.3. State the general processes for solving linear-programming exercises.
(SAQ 16.2)
16.4. Highlight the assumptions underlining linear model. (SAQ 16.3)
16.5. Outline the guidelines for formulating linear programming model. (SAQ
16.4)
Key words;linear programming, inequalities, iterations, linear, programming, and
iterations.
16.1. Meaning, Formulation, and Structureof Linear Programming
16.1.1. Meaning of Linear Programming
Linear programming is the process of taking various linear inequalities relating to some
situation, and finding the "best" value obtainable under those conditions. A typical
example would be taking the limitations of materials and labor, and then determining the
"best" production levels for maximal profits under those conditions.In "real life", linear
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programming is part of a very important area of mathematics called "optimization
techniques". This field of study (or at least the applied results of it) are used every day in
the organization and allocation of resources. These "real life" systems can have dozens or
hundreds of variables, or more. In algebra, though, you'll only work with the simple (and
graphable) two-variable linear case.The general process for solving linear-programming
exercises is to;
1. graph the inequalities (called the "constraints") to form a walled-off area on the
x,y-plane (called the "feasibility region").
2. then you figure out the coordinates of the corners of this feasibility region (that is,
you find the intersection points of the various pairs of lines), and
3. test these corner points in the formula (called the "optimization equation") for
which you're trying to find the highest or lowest value.
The most important feature of linear programming is the presence of linearity in the
problem. The various models in linear programming are:
a. Simplex method
b. Transportation model
c. Assignment model
In a linear programming problem, we are given a set of variables, and we want to assign
real values to them to; satisfy a set of linear equations and/or linear inequalities involving
these variables and; maximize or minimize a given linear objective function.
Box 16.1. The general process for solving Linear Programming exercises are;
1. Graph the inequalities (called the "constraints") to form a walled-off area on the x,y-
plane (called the "feasibility region").
2. Figure out the coordinates of the corners of this feasibility region (that is, you find the
intersection points of the various pairs of lines), and
3. Test these corner points in the formula (called the "optimization equation") for which
you're trying to find the highest or lowest value.
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If you are to find the maximal and minimal value of z = 3x + 4y subject to the following constraints:
The three inequalities in the curly braces are the constraints. The area of the plane that
they mark off will be the feasibility region. The formula "z = 3x + 4y" is the optimization
equation. I need to find the (x, y) corner points of the feasibility region that return the
largest and smallest values of z.My first step is to solve each inequality for the more-
easily graphed equivalent forms:
To find the corner points, which are not always clear from the graph; we shall pair the lines (thus forming
a system of linear equations) and solve:
y = –( 1/2 )x + 7
y = 3x
y = –( 1/2 )x + 7
y = x – 2
y = 3x
y = x – 2
–( 1/2 )x + 7 = 3x
–x + 14 = 6x
14 = 7x
2 = x
y = 3(2) = 6
–( 1/2 )x + 7 = x – 2
–x + 14 = 2x – 4
18 = 3x
6 = x
y = (6) – 2 = 4
3x = x – 2
2x = –2
x = –1
y = 3(–1) = –3
corner point at (2, 6) corner point at (6, 4) corner pt. at (–1, –3)
So, the corner points are (2, 6), (6, 4), and (–1, –3).
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Somebody smart proved that, for linear systems like this, the maximum and minimum
values of the optimization equation will always be on the corners of the feasibility region.
So, to find the solution to this exercise, I only need to plug these three points into "z = 3x
+ 4y".
(2, 6): z = 3(2) + 4(6) = 6 + 24 = 30
(6, 4): z = 3(6) + 4(4) = 18 + 16 = 34
(–1, –3): z = 3(–1) + 4(–3) = –3 – 12 = –15
Then the maximum of z = 34 occurs at (6, 4), and the minimum of z = –15 occurs at (-1,
–3).
This made linear programming is a mathematical technique designed to aid managers in
allocating scarce resources (such as labor, capital, or energy) among competing activities.
It reflects, in the form of a model, the organization's attempt to achieve some objective
(frequently, maximizing profit contribution, maximizing rate of return, minimizing cots)
in view of limited or constrained resources (available capital or labor, service levels,
available machine time, budgets). The linear programming technique can be said to have
a linear objective function that is to be optimized (either maximized or minimized)
subject to linear equality or inequality constraints and sign restrictions on the variables.
The term linear describes the proportionate relationship of two or more variables. Thus, a
given change in one variable will always cause a resulting proportional change in another
variable.
Some areas in which linear programming have been applied will be helpful in setting the
climate for learning about this important technique. Linear programming will be useful
when;
• A company produces agricultural fertilizers. It is interested in minimizing costs
while meeting certain specified levels of nitrogen, phosphate, and potash by
blending together many raw materials.
• An investor wants to maximize his or her rate of return by investing in stocks and
bonds. The investor can set specific conditions that must be met including
availability of capital.
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• A company wants the best possible advertising exposure among many national
magazines, and radio and television commercials within its available capital
requirements.
• An oil refinery blends several raw gasoline and additives to meet a car
manufacturer's specifications while still maximizing its profits.
• A city wants to maximize the day time use of recreational properties being
proposed for purchase with a limited capital available.
This technique, called linear programming (L.P), is solved in a step-by-step manner
called iterations. Each step of the procedure is an attempt to improve on the solution
until the" best answer" is obtained or until it is shown that no feasible answer exists.
In-text Question
• Do you think the term linear describes the proportionate relationship of two or
more variables? Support your answer with a sentence.
o Yes, because a given change in one variable will always cause a resulting
proportional change in another variable.
16.1.2. Formulation of the Linear Programming Problem
To formulate a real-life problem as a linear program is an art. To aid you in this task, it is
helpful to isolate the essential elements of the problem as a means of asking what the
clients wants and what information can be gained from the data that has been
provided.Linear Programming is a mathematical technique for optimum allocation of
limited or scarce resources, such as labour, material, machine, money, energy and so on,
to several competing activities such as products, services, jobs and so on, based on a
given criteria of optimality.
The term ‘Linear’ is used to describe the proportionate relationship of two or more
variables in a model. The given change in one variable will always cause a resulting
proportional change in another variable.The word, ‘programming’ is used to specify a
sort of planning that involves the economic allocation of limited resources by adopting a
course of action or strategy among various alternatives strategies to achieve the desired
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objective.Hence, Linear Programming is a mathematical technique for optimum
allocation of limited or scarce resources, such as labour, material, machine, money
energy etc.
16.1.3. Structure of Linear Programming model
The general structure of the Linear Programming model essentially consists of three
components.
� The activities (variables) and their relationships
� The objective function and
� The constraints
The activities are represented by X1, X2, X3 …….Xn.
These are known as Decision variables.
The objective function of an LP (Linear Programming Problem) is a mathematical
representation of the objective in terms a measurable quantity such as profit, cost,
revenue, etc.
Optimize (Maximize or Minimize) Z=C1X1 +C2X2+ ……….Cn Xn
Where Z is the measure of performance variable
X1, X2, X3, X4….Xn are the decision variables
And C1, C2, …Cn are the parameters that give contribution to decision variables.
These are the set of linear inequalities and/or equalities which impose restriction of the
limited resources.
In-text Question
• In Linear Programming, what do you think the word programming stands for?
o The word, ‘programming’ is used to specify a sort of planning that involves the
economic allocation of limited resources by adopting a course of action or
strategy among various alternatives strategies to achieve the desired objective.
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16.2. Assumptions of Linear Programming Certainty
In all LP models, it is assumed that all the model parameters such as availability of
resources, profit (or cost) contribution of a unit of decision variable and consumption of
resources by a unit of decision variable must be known and constant. Some of the
assumptions are;
1. Divisibility (Continuity)
The solution values of decision variables and resources are assumed to have either whole
numbers (integers) or mixed numbers (integer or fractional). However, if only integer
variables are desired, then Integer programming method may be employed.
2. Additivity
The value of the objective function for the given value of decision variables and the total
sum of resources used, must be equal to the sum of the contributions (Profit or Cost)
earned from each decision variable and sum of the resources used by each decision
variable respectively. The objective function is the direct sum of the individual
contributions of the different variables.
3. Linearity
All relationships in the LP model (i.e. in both objective function and constraints) must be
linear.
16.2.1. General Mathematical Model of an LPP
Optimize (Maximize or Minimize) Z=C1 X1 + C2 X2 +……+CnXn
Subject of constraints,
a1X1+ a 12X2+………………+ a 1nXn (<,=,>) b1
a21X1+ a 2X2+………………+ a 2nXn (<,=,>) b2
a31X1+ a 32X2+………………+ a 3nXn (<,=,>) b3
am1X1+ a m2X2+………………+ a mnXn (<,=,>) bm
and X1, X2 ….Xn >
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Box 16.2. Assumptions of Linear Programming Certainty
The assumptions of Linear Programming certainty are;
1. Divisibility
2. Additivity
3. Linearity
As we conclude this course, let us briefly examine the guidelines for formulating Linear Programming
Model
16.2.2. Guidelines for Formulating Linear Programming Model
The guidelines are;
1. Identify and define the decision variable of the problem.
2. Define the objective function.
3. State the constraints to which the objective function should be optimized (i.e.
Maximization or Minimization).
4. Add the non-negative constraints from the consideration that the negative values
of the decision variables do not have any valid physical interpretation.
Let us consider this example;
Example 1
A manufacturer produces two types of models M1 and M2.Each model of the type M1
requires 4 hours of grinding and 2 hours of polishing; whereas each model of M2 requires
2 hours of grinding and 5 hours of polishing. The manufacturer has 2 grinders and 3
polishers. Each grinder works for 40 hours a week and each polisher works 60 hours a
week. Profit on M1 model is N3.0 and on model M2 is N4.0.Whatever produced in a
week is sold in the market. How should the manufacturer allocate his production capacity
to the two types of models, so that he makes maximum profit in a week?
a. Identify and define the decision variable of the problem. Let X1 and X2 be the
number of units of M1 and M2 model.
b. Define the objective function since the profits on both the models are given, the
objective function is to maximize the profit.Max Z = 3X1 + 4X2
c. State the constraints to which the objective function should be optimized (i.e.
Maximization or Minimization).
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There are two constraints one for grinding and the other for polishing.The grinding
constraint is given by
4X1 + 2X2 < 80
No of hours available on grinding machine per week is 40 hrs. There are two grinders.
Hence the total grinding hour available is 40 X 2 = 80 hours.
The polishing constraint is given by
2X1 + 5X2 < 180
No of hours available on polishing machine per week is 60 hrs. There are three grinders.
Hence, the total grinding hour available is 60 X 3 = 180 hours.
Finally, we have,
Max Z = 3X1 + 4X2
Subject of constraints,
4X1 + 2X2 < 80
2X1 + 5X2 < 180
X1, X2 > 0
Summary of Session 16
In this lecture, you have learned that;
1. Linear programming is the process of taking various linear inequalities relating to
some situation, and finding the "best" value obtainable under those conditions.
2. The most important feature of linear programming is the presence of linearity in
the problem. The various models in linear programming are: simplex method;
transportation model; and assignment model.
3. The linear programming technique can be said to have a linear objective function
that is to be optimized (either maximized or minimized) subject to linear equality
or inequality constraints and sign restrictions on the variables.
4. This technique, called linear programming (L.P), is solved in a step-by-step
manner called iterations. Each step of the procedure is an attempt to improve on
the solution until the" best answer" is obtained or until it is shown that no feasible
answer exists.
5. The term ‘Linear’ is used to describe the proportionate relationship of two or more
variables in a model. The given change in one variable will always cause a
resulting proportional change in another variable.
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6. The word, ‘programming’ is used to specify a sort of planning that involves the
economic allocation of limited resources by adopting a course of action or strategy
among various alternatives strategies to achieve the desired objective.
7. The assumptions of linear programming certainty are; divisibility; additivity; and
linearity.
8. General Mathematical Model of an LPP is
Optimize (Maximize or Minimize) Z=C1 X1 + C2 X2 +……+CnXn
Subject o constraints,
a1X1+ a 12X2+………………+ a 1nXn (<,=,>) b1
a21X1+ a 2X2+………………+ a 2nXn (<,=,>) b2
a31X1+ a 32X2+………………+ a 3nXn (<,=,>) b3
am1X1+ a m2X2+………………+ a mnXn (<,=,>) bm
and X1, X2 ….Xn >
Self-Assessment Questions (SAQs) for Session 16
Now that you have completed this study session, you can assess how well you have
achieved its Learning Outcomes by answering these questions. You can check your
answers with the Notes on the Self-Assessment Questions at the end of this courseware.
SAQ 16.1. (tests learning outcomes 16.1. and 16.2)
In the statements provided here, fill the blanks with the most appropriate keywords
a. __________ is the process of taking various linear inequalities relating to some
situation, and finding the "best" value obtainable under those conditions.
b. In Linear Programming, constraints can also be called ___________.
c. The term _________is used to describe the proportionate relationship of two or
more variables in a model.
d. The word, __________ is used to specify a sort of planning that involves the
economic allocation of limited resources by adopting a course of action or strategy
among various alternatives strategies to achieve the desired objective.
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SAQ 16.2. (tests learning outcome 16.3.)
As we have discussed in this lecture, what are the general process involved when solving
linear-programming exercises?
SAQ 16.3. (tests learning outcome 16.3.)
In Linear Programming, what are the assumptions guiding model parameters such as
availability of resources, and profit (or cost) contribution of a unit of decision variable?
SAQ 16.3. (tests learning outcome 16.3.)
As an expert in Management, you have been saddled with the task of formulating a linear
programming model. In doing this, what are some of the guidelines you need to strictly
adhere to?
And this brings us to the end of this course. I want to believe you have been able to learn
the essential skills and broadened your knowledge of Operations Management in
Educational Practice. I wish you all the best in your studies….
References
Cohen, J., Cohen P., West, S.G., and Aiken, L.S. 2003. Applied multiple
regression/correlation analysis for the behavioral sciences. (2nd ed.) Hillsdale,
NJ: Lawrence Erlbaum Associates.
Kaw, A. and Kalu, E. 2008, Numerical Methods with Applications (1st ed.), linear and
non-linear regression.
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APPENDIX
Notes to the Self-Assessment Questions (SAQs) for Session 1
SAQ 1.1.
a. TRUE
b. FALSE
SAQ 1.2.
Management has been practiced in some form or the other since the dawn of civilisation.
Ever since human beings began to live and work together in groups, techniques of
organisation and management were evolved.
SAQ 1.3.
Management thinking and practice have evolved over the last century because of
increased understanding of human and organisational behaviour, the economic climate
and historical context and the changes in generations over time.
SAQ 1.4.
The modern management activities are;
1. The empirical school: Studying experience to draw generalizations and to develop
means of teaching experiences to other practitioners and students.
2. The social school system: This stems from the application of behavioural sciences
to management.
3. The Decision theory school: This concentrates on rational approaches to decision
making-the selection of a course of action from various possible alternatives.
Notes to the Self-Assessment Questions (SAQs) for Session 2
SAQ 2.1.
a. evaluate and estimate
b. cost and time.
c. planning and coordinating.
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SAQ 2.2.
Program Evaluation and Review Technique (PERT) is a technique adopted by
organizations to analyze and represent the activity in a project and to illustrate the flow of
events in a project. PERT also illustrates the activities and interdependencies in a project.
The main goal of PERT is to reduce the cost and time needed to complete a project.
SAQ 2.3.
The steps to follow are; Identifying tasks and milestones; Placing the tasks in a proper
sequence; Network diagramming; Time estimating and Critical Path estimating.
SAQ 2.4.
The project information input into the computer includes; the earliest start time for each
activity; earliest finish time for each activity; latest start time for each activity; and latest
finish time for each activity without delaying the project completion.
Notes to the Self-Assessment Questions (SAQs) for Session 3
SAQ 3.1.
a. Planning, scheduling, and controlling.
b. Float time
SAQ 3.2.
The critical path method (CPM) is a step-by-step technique for process planning that
defines critical and non-critical tasks with the goal of preventing time-frame problems
and process bottlenecks.
SAQ 3.3.
The key steps in critical path method are;
1. Activity specification
2. Activity sequence establishment
3. Network diagram
4. Estimates for each activity
5. Identification of the critical path; and
6. Critical path diagram to show project progresses.
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SAQ 3.4.
Some of the benefits to be derived are;
a. Offers a visual representation of the project activities.
b. Presents the time to complete the tasks and the overall project.
c. Tracking of critical activities.
On the other hand, the limitations are;
a. Less focus on non-critical tasks that can cause risk.
b. Based on only deterministic task duration.
c. Critical Path can change during execution.
SAQ 3.5.
CCPM is relevant to CPM in the sense that it helps to surmount the limitations facing
CPM.
Notes to the Self-Assessment Questions (SAQs) for Session 4
SAQ 4.1.
a. FALSE
b. TRUE
c. TRUE
SAQ 4.2.
An inventory policy is a standard set of rules/boundaries and guidelines that provide the
framework for an organisation to make better informed and timely decisions on which
stock to purchase or manufacture, how much stock to purchase or manufacture and where
to store and distribute to customers. The methods best suited for organisations are;
Reorder point; Min/Max; lot for lot; days of supply and item location.
SAQ 4.3.
Days of Supply, Demand-Based Days of Supply (DOS) - Demand is similar to an s,S
inventory policy except that the parameters for minimum and maximum levels are
specified in number of days rather than product quantities. This policy computes the daily
average of product by looking back at the actual demand. How far back to look is given
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by the DOS window field while Days of Supply, Forecast-Based DOS is similar to an s,S
inventory policy except that the parameters for minimum and maximum levels are
specified in number of days rather than product quantities. This policy computes the daily
average of product by looking forward and using forecasted demand.
SAQ 4.4.
The needed strategies are;
1. Direct deliveries of purchase products in raw material or assembly form can be
delivered to a manufacturing line or processing point and avoid double handling
through a warehouse process.
2. Just in time production by only making what is required resulting in lower WIP
inventory.
3. Direct Deliveries of finished goods by shipping direct from your source of supply
and avoiding your logistics network, if possible.
Notes to the Self-Assessment Questions (SAQs) for Session 5
SAQ 5.1.
a. TRUE
b. FALSE
c. TRUE
d. FALSE
e. TRUE
SAQ 5.2.
Items that deteriorate are likely to be large and costly (e.g., machine tools, trucks, ships,
and home appliances). Non-deteriorating items tend to be small and relatively
inexpensive (e.g., light bulbs, vacuum tubes, ink cartridges). The longer a deteriorating
item is operated the more maintenance it requires to maintain efficiency.
SAQ 5.3.
The NPV is the value obtained by discounting all cash outflows and inflows of an
investment opportunity by a chosen rate of return. The NVP valuation method requires
estimating the size and timing of all the incremental cash flows from the project. These
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future cash flows are then discounted to determine their present value. Some of the uses
to management are; it considers the time value of money; it is an absolute measure of
return; it uses cash flows and not profits; and it considers the whole life of the project.
Notes to the Self-Assessment Questions (SAQs) for Session 6
SAQ 6.1
1. B
2. D
3. A
4. A
5. C
SAQ 6.2.
Queuing theory is the mathematical study that deals with problems which involve
queuing (or waiting lines), or queues. In queuing theory, a model is constructed so that
queue lengths and waiting times can be predicted.
SAQ 6.3.
Here are some of the major points that will be raised in the report;
1. Analysing the arrival process
2. Checking the service mechanism
3. Examining the queue characteristics. (See Session for details)
Notes to the Self-Assessment Questions (SAQs) for Session 7
SAQ 7.1.
a. Process
b. Implementation
c. TQM
d. Profitability and Competitiveness
e. Technical and Operational
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SAQ 7.2.
Some of the pioneers in the origin of TQM are;
1. Total Quality Management (TQM)in the form of statistical quality control was
invented by Walter A. Shewhart.
2. TQM was demonstrated on a grand scale by Japanese industry through the
intervention of W. Edwards Deming with the help of missionary labors in the U.S.
and across the world.
3. TQM in education surfaced in 1988 at Mt. Edgecombe High school in Sitka,
Alaska when David Langford the school’s technology teacher/coordinator, applied
Total Quality concepts in his classes.
SAQ 7.3.
Total Quality Management (TQM) refers to management methods used to enhance
quality and productivity in profit making organizations. In other words, Total Quality
Management (TQM) describes a management approach to long–term success through
customer satisfaction. Like many of these other systems, TQM provides a framework for
implementing effective quality and productivity initiatives that can increase the
profitability and competitiveness of organizations.
SAQ 7.4.
The elements of TQM are; Customer-focused; Total employee involvement; Process-
centered; Integrated system; Strategic and systematic approach; Continual improvement;
Fact-based decision making and Communication.
SAQ 7.5.
Some of the generic models in TQM are;
1. Top management learns about and decides to commit to TQM. TQM is identified
as one of the organization’s strategies.
2. The organization assesses current culture, customer satisfaction, and quality
management systems.
3. Top management identifies core values and principles to be used, and
communicates them.
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4. A TQM master plan is developed based on steps 1, 2, and 3.
5. The organization identifies and prioritizes customer demands and aligns products
and services to meet those demands.
6. Management maps the critical processes through which the organization meets its
customers’ needs.
Notes to the Self-Assessment Questions (SAQs) for Session 8
SAQ 8.1.
There are problems where certain facilities must be assigned to specified jobs to
maximize the overall performance of the assignment. The Hungarian Method can also
solve such assignment problems, as it is easy to obtain an equivalent minimization
problem by converting every number in the matrix to an opportunity loss.
SAQ 8.2.
For Minimization, the steps are;
STEP 1: Identify the minimum element in each row and subtract it from every element
of that row, we get the reduced matrix.
STEP 2: Identify the minimum element in each column and subtract it from every
element of that column
STEP 3: Make the assignment for the reduced matrix obtain from steps 1 and 2
For Maximization;
STEP 1: Subtract the smallest entry in each row from all the entries of its row.
STEP 2: Subtract the smallest entry in each column from all the entries of its column.
STEP 3: Draw lines through appropriate rows and columns so that all the zero entries of
the cost matrix are covered and the minimum number of such lines is used.
STEP 4: Test for Optimality: If the minimum number of covering lines is n, an optimal
assignment of zeros is possible and we are finished. If the minimum number of
covering lines is less than n, an optimal assignment of zeros is not yet possible.
In that case, proceed to Step 5.
STEP 5: Determine the smallest entry not covered by any line. Subtract this entry from
each uncovered row, and then add it to each covered column. Return to Step 3.
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SAQ 8.3.
1. 76
2. Maximum profit through this assignment is 214
Notes to the Self-Assessment Questions (SAQs) for Session 9
SAQ 9.1.
Supply, demand
SAQ 9.2.
The transportation problem is concerned with finding an optimal distribution plan for a
single commodity. A given supply of the commodity is available at a number of sources,
there is a specified demand for the commodity at each of the destinations, and the
transportation cost between each source-destination pair is known.There are two types of
Transportation Problem namely:
1. Balanced Transportation Problem and
2. Unbalanced Transportation Problem.
SAQ 9.3.
The following variants are being considered in simplex method;
i. Minimization
ii. Inequality in the wrong direction
iii. Degeneracy
iv. Unbounded solution
v. Multiple solutions
vi. Non-existing feasible solution
vii. Unrestricted variables
SAQ 9.4.
The transportation method consists of the following three steps.
1. Obtaining an initial solution, and making an initial assignment in such a way that a
basic feasible solution is obtained.
2. Ascertaining whether it is optimal or not, by determining opportunity costs
associated with the empty cells, and if the solution is not optimal.
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3. Revising the solution until an optimal solution is obtained.
Notes to the Self-Assessment Questions (SAQs) for Session 10
SAQ 10.1
The steps needed are;
1. Select the north west (upper left-hand) corner cell of the transportation table and
allocate as many units as possible equal to the minimum between available supply
and demand requirements, i.e., min (s1, d1).
2. Adjust the supply and demand numbers in the respective rows and columns
allocation.
3. If the supply for the first row is exhausted, then move down to the first cell in the
second row.
4. If the demand for the first cell is satisfied, then move horizontally to the next cell
in the second column.
5. If for any cell supply equals demand, then the next allocation can be made in cell
either in the next row or column.
6. Continue the procedure until the total available quantity is fully allocated to the
cells as required.
SAQ 10.2.
1a. Total cost= 20(21) + 30(18) + 30(24) + 30(20) + 25(25) +25(25) =
630+540+720+600+625+625 = N3740
1b. N 30
1c. N40
2. 5(400) + 8(400) + 7(300) + 7(300) + 7(530) +5(550) = 2000+ 3200+ 2100+ 2100+
3710 + 2750 = N15,925
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Notes to the Self-Assessment Questions (SAQs) for Session 11
SAQ 11.1.
The steps in Least-cost method are;
1. Assign as much as possible to the cell with the smallest unit cost in the entire
table. If there is a tie, then choose arbitrarily.
2. Cross out the row or column which has satisfied supply or demand. If a row and
column are both satisfied, then cross out only one of them.
3. Adjust the supply and demand for those rows and columns which are not crossed
out.
4. When exactly one row or column is left, all the remaining variables are basic and
are assigned the only feasible allocation.
Notes to the Self-Assessment Questions (SAQs) for Session 12
SAQ 12.1.
The steps in VAM are;
1. Identify the boxes having minimum and next to minimum transportation cost in
each row and write the difference (penalty) along the side of the table against the
corresponding row.
2. Identify the boxes having minimum and next to minimum transportation cost ineach
column and write the difference (penalty) against the corresponding column.
3. Identify the maximum penalty. If it is along the side of the table, make maximum
allotment to the box having minimum cost of transportation in that row. If it is
below the table, make maximum allotment to the box having minimum cost of
transportation in that column.
4. If the penalties corresponding to two or more rows or columns are equal, select the
top most row and the extreme left column.
Notes to the Self-Assessment Questions (SAQs) for Session 13
SAQ 13.1.
a. Model
b. Management model
c. Analogue model
d. Physical and graphic model
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e. Deduction
f. Inductive
SAQ 13.2.
A model is a simplified representation of the real world and as such includes only those
variables relevant to the problem at hand.There are four patterns of model construction,
only two of which involve experimentation: inspection, use of analogues, operational
analysis, and operational experiments. They are considered here in order of increasing
complexity. In some cases, the system and its problem are relatively simple and can be
grasped either by inspection or from discussion with persons familiar with it. In general,
only low-level and repetitive operating problems, those in which human behaviour plays
a minor role can be so treated.
SAQ 13.3.
Procedures for deriving solutions from models are either deductive or inductive. With
deduction one moves directly from the model to a solution in either symbolic or
numerical form. Inductive procedures involve trying and comparing different values of
the controlled variables. (See Session for details)
SAQ 13.4.
The Model Building Processes are:
• Compute the background equation
• Analyze the factors available to explain the difference between actual effort and
effort as predicted by the background equation
• Use this model to predict the effort for the new project
SAQ 13.5.
• The steps in Lewin's management model are; unfreeze, transition, and refreeze.
• The factors in Mckinsey 7s Model are; shared values; strategy; structure; systems;
style; staff and skills.
• The steps available in Kotter's 8 step model are;
1. Increase the urgency for change.
187
2. Build a team dedicated to change.
3. Create the vision for change.
4. Communicate the need for change.
5. Empower staff with the ability to change.
6. Create short term goals.
7. Stay persistent.
8. Make the change permanent.
Notes to the Self-Assessment Questions (SAQs) for Session 14
SAQ 14.1.
a. Decision-making
b. Programmed decision
c. Non-programmed decision
d. Group
e. Decision making
SAQ 14.2.
Decision making is the cornerstone of planning because it is the catalyst that drives the
planning process. An organization’s goals follow from decisions made by various
managers. Furthermore, in deciding to adopt the best plan for achieving goals, decision
making basically reflects the selection of the best choice among possible alternatives and
putting it into practice.
SAQ 14.3.
1. Programmed decision
2. Non-programmed decision
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SAQ 14.4.
The procedures in PPBS are;
1. Decision-Making under states of Certainty, Uncertainty and Risk
2. Proactive and Reactive Decisions
3. The Rational Decision Making Process
4. Individual Decision Making
5. A Group Decision-Making
SAQ 14.5.
Some of the decision-making techniques are;
1. Brainstorming
2. The Delphi Technique
3. The Nominal Group Technique (NGT)
4. Marginal Analysis
5. Cost benefit or cost effectiveness analysis.
Notes to the Self-Assessment Questions (SAQs) for Session 15
SAQ 15.1.
a. Goal setting and planning
b. Top down process
c. Bottom up process
SAQ 15.2.
a. It refers to a formal set of procedures that begins with goal setting and continues
through performance review.
b. Managers and those they supervise act together to set common goals.
c. Each person’s major areas of responsibility are clearly defined in terms of
measurable expected results or objectives. These are used by subordinates in
planning their work.
d. At periodic intervals, the expected results or objectives jointly set by managers
and their subordinates are used to monitor and review progress.
e. Based on the agreed objectives or results, the performance of subordinates is
evaluated.
189
SAQ 15.3.
We have the following in the process;
1. Organizational goals are developed based on organizational missions.
2. Specific goals are established for departments, subunits, and individuals.
3. Action plans are formulated, describing what is to be done, how, when, where, and
by whom to achieve a goal.
4. Individuals are given the responsibility of reaching their objectives and that goals
will ultimately be met.
5. Performance is appraised at the end of the goal-setting cycle, typically at one-year
intervals. Praise, recognition, and rewards should be given for effective
performance.
SAQ 15.4.
The elements are;
a. Goal specificity
b. Participative decision making
c. Explicit time-period
d. Performance feedback
Notes to the Self-Assessment Questions (SAQs) for Session 16
SAQ 16.1.
a. Linear programming
b. Inequality
c. Linear
d. Programming
SAQ 16.2.
The general process for solving linear-programming exercises is to;
1. graph the inequalities (called the "constraints") to form a walled-off area on the
x,y-plane (called the "feasibility region").
2. then you figure out the coordinates of the corners of this feasibility region (that is,
you find the intersection points of the various pairs of lines), and
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3. test these corner points in the formula (called the "optimization equation") for
which you're trying to find the highest or lowest value.
SAQ 16.3.
The assumptions of Linear Programming certainty are;
1. Divisibility
2. Additivity
3. Linearity
SAQ 16.4.
The guidelines are;
1. Identify and define the decision variable of the problem.
2. Define the objective function.
3. State the constraints to which the objective function should be optimized (i.e.
Maximization or Minimization).
4. Add the non-negative constraints from the consideration that the negative values of
the decision variables do not have any valid physical interpretation.