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# Operation Research chapter 2

By Anita Andrews,2014-05-28 14:27
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Operation Research chapter 2

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Chapter 2 : Overview of the OR modeling Approach

Mathematical method of OR - quantitative techniques form the main part of what is known about OR. Usual phases of OR study is the following:

2011/1/31

Introduction to Operations Research

Page 1

OR

School of Management?CHUST

Usual Phase of OR Study

Define the problem of interest and gather relevant data. Formulate a mathematical model to represent the problem. Develop a computer-base procedure for deriving solution to the problem from the model. Test the model and refine it as needed. Prepare for the ongoing application of the model as proscribed implement

2011/1/31 Introduction to Operations Research Page 2

OR

School of Management?CHUST

2.1 Define the Problem and Gather Data

Determining appropriate objective for the problem to be considered.

For entire organization, usually the objective that are formulated should be those of entire organization ?C OR study seeks solution that are optimal for overall organization rather than suboptimal solution that are best for only one component. For profit-making organization, OR study use long-run profit maximization as the sole objective. However, many profit-making organization do not use this approach and use satisfactory profits combined with other objective.

2011/1/31 Introduction to Operations Research Page 3

OR

School of Management?CHUST

2.1 Define the Problem and Gather Data

Gathering relevant data about the problem

OR team spend large amount of time gathering relevant data to provide the needed input of the mathematical model. Install a new Management Information System to collect the necessary data and spend time trying to improve the precision of the data.

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OR

School of Management?CHUST

2.2 Formulating A mathematical Model

OR approach for constructing a mathematical model that represent the essence of the problem defined by the decision maker.

Models ?C idealized representation, play an important role in science and business. Mathematical Models are expressed in terms of mathematical symbol and expression. Mathematical model of a business problem is the system of equation and related mathematical expression that represent the essence of the problem.

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OR

School of Management?CHUST

2.2 Formulating A mathematical Model

Decision variables. If there are n related quantifiable decision to be made, they are represented as decision variable (x1 x2 ????xn) whose respective value are to be determined. Objective function, Appropriate measure of performance is expressed as a mathematical function of decision variable. Constraints, Mathematical expression for the restriction. Any restriction on the value that can be assigned to decision variable are also expressed mathematically, typically by means of inequalities or equations.

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OR

School of Management?CHUST

2.2 Formulating A mathematical Model

Linear Programming model. Both the objective function and constraints are all linear functions of decision variable. Advantage of Mathematical Model:

Describes a problem much more concisely. Forms a bridge to the use of high-powered mathematical techniques and computer to analyze the problem. packaged software for personal computer has become wide available for solving many model.

Requirement of Mathematical Model.

Valid representation of the problem; Be tractable (capable of being solved) abstract idealization of the problem, simplify assumption.

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OR

School of Management?CHUST

2.2 Formulating A mathematical Model

Examples: A mathematical model for Monsanto Corp. problem decision variables: objective function: Constraint:

r

R ij

?Æ ?Æc R

i =1 j =1 ij

r

s

ij

?Æ?Æ p R

i =1 j =1 s ij

s

ij

?ÝT

?ÆR

j =1

ij

=1

Parameter cij , pij ?C coefficient of decision variable

2011/1/31 Introduction to Operations Research Page 8

OR

School of Management?CHUST

2.3 Deriving Solution from the model

To develop a procedure (a computer-based procedure) for deriving solution to the problem from this model. Standard Algorithm (systematic solution procedure) of OR Many procedure have been developed to get the optimal or best solution of the problem. Since the model is an idealized rather than an exact representation of real problem, optimal solution for the model cannot be the best possible solution for the real problem. If the model is well formulated and tested, the optimal solution should tend to be a good approximation to an idea course of action for the real problem.

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OR

School of Management?CHUST

2.3 Deriving Solution from the model

Some management scientist point out: satisficing is much more prevalent than optimizing in actual practice. Distinction between ??optimizing?? and ??satisficing?? reflects the difference between theory and realities. OR team attempt to bring as much of the ??science of ultimate?? as possible to the decision-making process. OR team sometime use only heuristic procedure to find a good suboptimal solution (because the time or cost required to find an optimal solution maybe very large). Great progress has been made in developing efficient

heurist procedure in recent years.

2011/1/31 Introduction to Operations Research Page 10

OR

School of Management?CHUST

2.3 Deriving Solution from the model

Postoptimality analysis (analysis done after finding a optimal solution ) is very important part for OR study. What-if-analysis. address question about what would happen to the optimal solution if different assumption are made about future condition. Sensitivity analysis. Value assigned to a parameter is just an estimate of some quantity, whose exact value will become know only in future.

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OR

School of Management?CHUST

2.4 Testing the Model

Usually the first version of large mathematical model contain many flaws ?C parameter have not been estimated correctly because the difficulty of collecting reliable data, forget some restrictions.

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OR

School of Management?CHUST

2.4 Testing the Model

Model Validation. Before using the model, OR team must test the model and try to identify or correct as many flaws as possible, Reexamining the definition of problem and comparing it with the model, mathematical expression. Retrospective Test ?C using historical data to reconstruct the past and then determining how well the model.

Comparing the effectiveness. by using alternative solution from the model and estimating their hypothetical historians performance Disadvantage of retrospective test is use the same data that guided the formulation of the model.

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OR

School of Management?CHUST

2.5 Preparing to Apply the Model

Install a well documented system for applying the model as proscribed by management, this system will include model, solution procedure, and operating procedure. For implementation a decision support system help

manager to use data and models to support (rather than replace) their decision making as needed.

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School of Management?CHUST

2.6 Implementation

OR study implement this system as prescribed by management. Both to make sure that model solution are accurately translated to an operating procedure and to rectify any flaws in the solution. Success of the implementation phase depend upon the support of both top management and operating management. OR team need good communication to ensure the study accomplish what management wanted.

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OR

School of Management?CHUST

2.6 Implementation

First, OR team give operating management a careful explanation of the new system to be adopted. Next, two parties share the responsibility for developing the procedure required to put this system into operation. during the new system is being used, OR team need continue to obtain feedback on how well system is working or the assumptions of the model continue to be satisfied. If significant deviations from the original assumptions occur, must modify the model in the system.

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OR

School of Management?CHUST

2.7 Conclusions

This book we focuses on constructing and solving mathematical model.

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OR

School of Management?CHUST

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