chapter 1 - introduction to or
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BAHIRDAR UNIVERSITYINSTITUTE OF TECHNOLOGY
SCHOOL OF MECHANICAL AND INDUSTRIAL ENGINEERING
Pr oduct i on Engineer i ng and Management M.Sc Pr ogr am
ADVANCED OPERATIONS RESEARCH
ns ruc or : mare a e u r
PhD in Industrial Engineering
.
B.Sc in Textile Engineering
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OBJECTIVES OF THE COURSE
1. Introduce different quantitative techniques fordecision making process.
2. Provide rational basis for decision making by
seeking to understand and structure complexsituations.
3. Introduce advanced concepts to optimize the
scarce resources.
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What is expected from you?
You are encouraged to study with friends, but you are
expected to compose your own reports.
ou are expecte to respon to quest ons as e y t e
Instructors) during lectures/tutorials.
ugges ons, commen s:
Directly to Instructors via Student Representative
I dont expect any specific knowledge, but I do expect an
open a u e o ngs.
I expect you to read moreand know by your own effort.
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History of Operations Research
s a re a ve y new sc p ne.
It is generally agreed that OR came into existence as a
critical need to manage scarce resources.
and engineers to analyze several military problems
Management of convoy, bombing, antisubmarine,
. The result was called Military Operations Research,
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ORoriginated in Great Britain during World War IIto bring mathematical or quantitative approaches
.
( Started in the UK and developed in the USA)
sta s ment o teams o sc ent sts to stu y t e
strategic and tactical problems involved in military
operations.
The ob ective was to find the most effective
utilization of limited military resources by the use
.
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There arethree important factors behind the rapid
1. The economic and industrial boom after World war II
resulted in continuous mechanization and
automation.2. Many Operations Researchers continued their
research after World war II.
3. Analytic power was made available by high-speedcomputers.
During 1950s, there was substantial progress in the
app ication o OR tec niques or Civi ian activitiesalong with great interest in the professional
.
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In 1948, OR club was formed in England which later
of UK.
Durin OR foundation, its rimar a lications
were: To support military operations: such as to support
radar systems, against submarine, etc.
Following the war, numerous peacetime applicationsemer e , ea n o e use o an mana emen
science in many industries and occupations.
,(ORSA) was founded.
B 1960s OR rou s were formed in several
organizations.Amare Matebu (Dr.) - BDU IOT
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This analytical approach is known by several different
names:
Operations Research (OR)
Operational Research (UK)
Systems Science
Mathematical Modeling
Industrial Engineering
Critical Systems strategic thinking
Success Science S and S stems Anal sis and Desi n
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Because ofOR s multi-disciplinary characterandapplication in varied fields,it has a bright future,
prov e peop e evo e o s u y can e p
meet the needs of society.
However, in order to make the future of OR
brighter, its specialists have to make good use of
the opportunities available to them.
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Definition of Operations ResearchDefinition of Operations Research
1. OR is the application of scientific methods, techniques
and tools to problems involving the operations of
systems so as to provide those in control of the
.
2. OR is the application of the scientific method to the
study of the operations of large, complex organizations
or activities.
3. OR is the application of the scientific method to the
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Definition - summary
ApplicationApplication of SCIENTIFICof SCIENTIFIC METHODMETHOD
StudyStudy ofof LARGE and COMPLEXLARGE and COMPLEX SYSTEMSSYSTEMS
na ys sna ys s oo
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Application of Operations Research
- Aggregate production planning, assembly line, blending, inventory control
- Employment, training, layoffs and quality control
- Transportation, planning and scheduling
Facilities planning
- Location and size of warehouse or new lant
- Logistics, layout and engineering design
- Transportation, planning and scheduling
- Capital budgeting, cost allocation and control, and financial planning
Marketing
- Sales effort allocation and assignment- Predicting customer loyalty
Purchasing, procurement and Exploration
- Optimal buying and reordering with or without price quantity discount
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Successful OR Applications
Com an Year Problem Techni ues Used
Annual
av ngs
Hewlett Packard 1998Designing buffers into
production li neQueuing models $280 mil l ion
Taco Bell 1998 Employee schedulingIP, Forecasting ,
$13 mil lion
Proctor & Gamble 1997
Redesign production &
distributon system Transportation models $200 mi ll ion
Delta Airl ines 1994 Assigning planes to routes Integer Programming $100 mil l ion
Queuin models,
Simulation
Yellow Freight
Systems, Inc.1992 Design trucking network
Network m odels,
Forecasting, Simulation$17.3 mil li on
San Francisco Police
Dept.
Bethlehem Steel 1989 Design an Ingot Mold Stripper Integer Programming $8 mil l ion
North Ameri can Van
Lines1988 Assigning loads to drivers Network modeling $2.5 mill ion
Citgo Petroleum 1987
distribution
,
Forecasting $70 mil lion
United Airl ines 1986Schedul ing reservation
personnelLP, Queuing, Forecasting $6 mi ll ion
Dair man's Creamer 1985 O timal roduction levels Linear Pro rammin $48 000
Phil l ips Petroleum 1983 Equipment replacement Network modeling $90,000
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Basics of Operations Research
Operations Research - Characteristics
Managerial decision making
System approach
Computers
Mathematical models
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OR provides rational basis for decision making:Solves the type of complex problems that turn
Builds mathematical and computer models of
organizational systems composed of people,
,
Uses analytical and numerical techniques to
make predictions and decisions based on these
models
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Why must we learn the decision-making process?"
Or anizations are becomin more com lex.
Environments are changing so rapidly that past
practices are no longer adequate.
The costs of making bad decisions have
increased.
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Optimization is Everywhere
It is embedded in language, and part of the way we
firms want to maximize value to shareholders
people want to make the best choices
When playing games, we want the best strategy
When we have too much to do, we want to
.
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Mathematical Optimization is nearly everywhere.
gr cu ture
Military
Production Management Financial Management
Marketing Management
Personnel Mana ement
Health care
Construction
, .
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Real World
Assumed Real World Model
Levels of abstraction in the model development
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requires the use of one or more mathematical
models.
ma ema ca mo e s a ma ema ca
representation of the actual situation that may
be used to make better decisions or clarify the
.
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Benefits of Modeling
Economy - it is often less costly to analyze decision
roblems usin models.
Timeliness - models often deliver needed information
more quickly than their real-world counterparts.
Feasibility - models can be used to do things that
would be impossible.
decision making.
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analysis
building
analysis tion
Feed back
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Methods of Operations Research
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Different Models
Linear Programming models
A single objective function, representing either a profit
to be maximized or a cost to be minimized, and a set of
.
The objective function and constraints all are linear
functions of the decision variables.
Software has been developed that is capable of solving
problems containing millions of variables and tens of
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Nonlinear Pro rammin models The objective and/or any constraint is nonlinear.
In general, much more difficult to solve than
linear.
Most (if not all) real world applications require a
nonlinear model.
In order to make the problems tractable, we
often approximate using linear functions.
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D namic Pro rammin A DP model describes a process in terms of states,
decisions, transitions and returns.
The rocess be ins in some initial state where a
decision is made.
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Stochastic models
In many practical situations the attributes of a
.
Examples include the number of customers in a
checkout line, congestion on a highway, the
,
a financial security are some of the stochastic.
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A stochastic process that can be observed at
regu ar nterva s suc as every ay or every wee
can be described by a matrix which gives the
probabilities ofmoving to each state from every
o er s a e n one me n erva .
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Simulation
It is often difficult to obtain a closed form
express on or e e av or o a s oc as c sys em.
Simulation is a very general technique for
estimating statistical measures of complex
sys ems.
A system is modeled as if the random variables
were known.
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The OR Problem Solving Schema
Formulation Monitoring
Realization
Modelling Implementation
olut onAnalysis
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St eps f or sol v i ng OR problem
Formulate the problem to be solved
Select appropriate tool necessary to solve the
problem
,
assumptions
Perform the analysis
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Solution:
Define decision variable
Let x1 and x2 be the number of hectors corn and potato grown
respectively, the following decision model represents the problem.
Max {w = 20,000X1 + 10,000X2} objective functions
Subject to:
20X1 + 40X2 200 (labor)
X1 + 4 (Environment) constraints
X2 3 (Crop rotation)
X1 + X2 6 (Land)
We will see more model buildin in the next cha ter.
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Mathematical Modeling and Optimization Building Blocks
data (Actual Situation and Requirements, Control Parameters)
e.g., number of sites, unit capacities, demand forecasts,
available resources
model (variables, constraints, objective function)
e.g., how much to produce, how much to ship, (decision
variables, unknowns)optimization algorithm and solver
e.g., simplex algorithm, B&B algorithm, outer approximation...
optimal solution (Suggested Values of the Variables)e.g., production plan, unit-connectivity, feed concentrations.
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Design Optimization
Optimization is a component of design process
The design of systems can be formulated as
roblems of o timization where a measure of
performance is to be optimized while satisfying
a t e constraints.
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D i O ti i ti
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Design Optimization
Design variables a set of parameters that describes
the system (dimensions, material, load, )
Design constraints all systems are designed to
.
constraints must be influenced by the design variables
(max. or min. values of design variables).
Objective function a criterion is needed to judge
whether or not a given design is better than another
, , , , , .
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O i i bl l i
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Optimum Design Problem Formulation
The formulation of an optimization problem is
extremely important, care should always be
exercised in defining and developing expressions
for the constraints.
The optimum solution will only be as good as the
.
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P bl F l ti (D i f t b t t )
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Problem Formulation (Design of a two -bar structure)
The problem is to design a two-member bracket to support a
force W without structural failure. Since the bracket will be
,
minimize its mass while also satisfying certain fabrication and
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Example Design of a Beer Can
beer and meet other design requirement. The cans will be
,
of manufacturing.Since the cost can be related directly tothe surface area of the sheet metal used, it is reasonable to
minimize the sheet metal required to fabricate the can.
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l i f C
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Example Design of a Beer Can
Fabrication, handling, aesthetic, shipping considerations
and customer needs impose the following restrictions on
the size of the can:
1. The diameter of the can should be no more than 8 cm.
Also, it should not be less than 3.5 cm.2. The height of the can should be no more than 18 cm
and no less than 8 cm.
3. The can is required to hold at least 400 ml of fluid.
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Example Design of a Beer Can
Design variables
D= diameter of the can cm
H= height of the can (cm)
Objective function
The design objective is to minimize the surface area
(Non-linear)
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Example Design of a Beer Can
The constraints must be formulated in terms of design variables.
The first constraint is that the can must hold at least 400 ml of fluid.
(Non-linear)
The other constraints on the size of the can are:
The problem has two independent design variable and five
near
exp c cons ra n s. e o ec ve unc on an rs
constraint are nonlinear in design variable whereas the
remaining constraints are linear.
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