1-intro to or.ppt

Prof Madya Pa’ezah HamzahOffice : S‐3‐27, FTMSKPhone: 03 – 5543 5476

012 – 213 5630

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Hillier F.S. & Lieberman, G.J. (2005) Introduction to Operations Research, 8th edition, McGraw‐Hill.

Winston W.L. (2004) Operations Research: Application and Algorithms, 4th edition, Duxbury Press, New York.

Chong Edwin K.P & Zak S. H (2008) An Introduction to Optimization, 3rd edition, Wiley International, 2008.

This course introduces students to the role of operations research in planning both in production and services. Students will be exposed to the linear and non‐linear programming models commonly used to allocate the best utilization of resources. The philosophy behind the theory will also be discussed to develop an understanding of the values and limitations of operations research as a tool in making wise decision in handling management and operational problems where resources are limited.

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1. Introduction to Operations Reasearch2. Linear Programming (Graphical Method,

Simplex Method, Computer Solutions)3. Transportation Problems4. Integer Programming5. Non‐Linear Programming6. Simulation

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Tests (2 tests) 30%Project/ Case Studies/ Presentation 30%Final examination 40%

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What is Operations Research?The relationship between Operations Research and Management Science.Historical perspective of Operations Research. Characteristics of Good DecisionOperations Research ModelsThe Operations Research Approach to Problem Solving

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You should be able todescribe the meaning of Operations Research (OR)list the OR approach to problem solving and explain each step.

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the scientific approach to decision making

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Input Data Scientific Model

Meaningful Output

Operational Research (in the UK)Management ScienceDecision ScienceQuantitative Analysis

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Scientific approach has been used in the managementof organizations.

The term OR arose in the 1940’s when research wascarried out by a group of scientists who successfullyused scientific methods to analyze military operationsduringWorldWar II (1939‐1945)

Main objective: to allocate scarce resources (e.g. millitary personnel, artilleries)effectively to win battles

Determine convoy size to minimize losses from submarine attacksDetermine the correct colour of aircraft to minimize detection by submarines, or to maximize the number of submarines sunkDetermine the best way to deploy radar units to maximize potemntial coverage

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After WWII, OR techniques gained popularity and were used to address decision problems in business, industry, and government.

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OR is now applied in many organizations to aid decision‐making.The growing complexity of management has necessitated the development of sophisticated mathematical techniques for planning and decision‐making.

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1. Development of numerous OR methods due to continued research.

2. Advancement in computing power due to digital computers.

George Dantzig developed the Simplex Method in 1947 to solve linear programming problem.

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OR has been recognized as a widely used decision‐making tools

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Forecasting: Using time series analysis to answer typical questions such as: How big will demand for products be? What are the sales patterns? How will this affect profits? Finance and Investment: How much capital do we need? Where can we get this? How much will it cost?Manpower planning and Assignment:How many employees do we need? What skills should they have? How long should they be doing their jobs?

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Sequencing and Scheduling:What job is most important? In what order should we do jobs? Location, Allocation, Distribution and Transportation:Where is the best location for an operation? How big should facilities be? What resources are needed? Are there shortages? How can we set priorities?

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Reliability and Replacement Policy: How well is equipment working? How reliable is it? When should we replace it? Inventory Control and Stockout:How much stock should we hold? When do we order more? How much should we order?

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Project planning and control:How long will a project take? What activities are most important? How should resources be used? Queuing and Congestion:How long are queues? How long do customers wait in line? How many servers should we use?

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OR is used to solve complex real‐world problems to arrive at optimal or good decision (sound judgment and good conclusions); it is not about the ideal. OR uses scientific methods – using procedures in manipulating raw data into meaningful information. OR is a practice for professionals.OR is interdisciplinary.

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Note: QMT437 focuses formulating models and getting solutions

Developing Model

Acquiring Input Data

Developing a Solution

Defining the Problem

Testing the Solution

Analyzing the Result

Implementing the Result

Develop clear and concise statement of the problem.Set objectives.Improperly defined problem can result in no solution or inappropriate solution.Set measurable objectives/goals to stay focus.

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Developing Model







Model= representation of a realityUsually a mathematical model

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Developing Model







Essential to obtain accurate data.Garbage in, garbage outSource of input data: company reports, documents, interview, etc.

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Developing Model







Manipulate data to arrive at best solution.How?

‐trial and error‐complete enumeration‐algorithm

Accuracy of the solution depends on the accuracy of the input data and the model

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Developing Model







To be done before a solution can beanalyzed and implemented.

Need testing because the solution dependson the input data and model. Collectadditional data from a different source, thencompare with the original data. Usestatistical tests to determine if there aredifferences. If there are significantdifferences, need to obtain more accurateinput data.

If data is accurate but results areinconsistent, the model may beinappropriate; validate the design of themodel. Make sure it is logical and representsthe real situation.

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Developing Model







Determine the implications of the solutionWhat implication will the solution have on the organization?Perform sensitivity analysis. Determine how solution will change if there were changes in the model or input

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Developing Model







The process of incorporating the solution into the organization.

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Develop Model

Acquire Input Data

Develop a Solution

Define the Problem

Test the Solution

Analyze the Result

Implement the Result

A model is a representation of reality (from the modeler's perspective)

Models can be Iconic ‐ static in nature; replicas, made to look like the real systemAnalog‐act like reality but often not appear like the realitySchematicSymbolic (Mathematical)

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Iconic Analog Mathematical(replicas, made to look like the real system)

-full-scale

-scaled-down

-scaled-up

(physical representation of non-physical object; act like reality but often not appear like reality )

e.g. thermometer

(mathematical relationships)

e.g.

profit=revenue-cost

y=mx+c

physical abstract

Schematic(drawings and pictures)

e.g. map, chart

OR approach to the decision‐making process is mostly through mathematical modeling.

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A firm makes a product that costs RM15 to produce and sells for RM20. 2 hours are required to produce each unit and only 40 hours of production time are available.Develop a model to calculate the total profit from selling the product

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A firm makes a product that costs RM15 to produce and sells for RM20. 2 hours are required to produce each unit and only 40 hours of production time are available.

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• Z and x are called variables

• Known, constant values which are often coefficients of variables are called parameters

Let Z = total profitx = units of the product to produce

Maximize Z = 20x – 15x subject to:

2x ≤ 40x ≥ 0

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Uncontrollable Inputs

(unit profit, 2 production hour/unit, 40 production-hr capacity)

Controllable Input

(x, the production qty)

Mathematical

Model

Maximize Z = 20x – 5xsubject to:

2x ≤ 40x ≥ 0

Output

(Z, the total profit; production time used)

Deterministic Model‐A model in which all values used in the model are known with complete certainty.

Probabilistic (Stochastic) Model‐A model in which at least one uncontrollable input is uncertain and subject to variation.

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As simple as possibleComplete and represent the problem accuratelyEasy to understandEasy to modify and updateRequired input data should be obtainable.

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1. Models can accurately represents reality if properly formulated.

‐ A valid model is one that is accurate and correctly represents the problem or system under investigation.

2. Models can help a decision maker formulate problems.

‐ e.g in profit model managers can determine important factors contributing to revenue and expenses.

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3. Models can give us insight and information. ‐ e.g. by performing sensitivity analysis to

study the impact of changes in a model

4. Models can test options without disrupting the real system.

5. Models can save time and money in decision making and problem solving.

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6. A model may be the only way to solve some large or complex problems in a timely manner.

7. A model can be used to communicate problems and solution to others.

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Conflicting viewpointsImpact on other departmentsManager’s perception of problems won’t match textbook approach; thus, OR analyst must be able to explain to managersNot understanding the modelDifficult to acquire good input data; lack of clean dataObtaining only one answerOutdated SolutionSolutions are not intuitively obvious, and rejected by managers Resistance to change; Lack of Commitment

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the meaning of Operations Research (OR)

the OR approach to problem solving

the meaning of the word model and the various types of model

the advantages of using models in problem solving

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Introduction to QM for Windows software

1-intro to or.ppt

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