Chapter 1 Introduction of OR

Chapter 1 Introduction of OR

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The Origins of Operations Research

Since the advent of the industrial revolution, the world has seen a remarkable growth in the size and complexity of organizations. One problem is a tendency for the many components of an organization to grow into relatively autonomous empires with their own goals and value systems, thereby losing sight of how their activities and objectives mesh with those of the overall organization.

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A related problem is that as the complexity and specialization in an organization increase, it becomes more and more difficult to allocate the available resources to the various activities in a way that is most effective for the organization as a whole.

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These kinds of problems and the need to find a better way to solve them provided the environment for the emergence of operations research.

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What is Operations Research? (1) Operation research is applied to problems

that concern how to conduct and coordinate the operations (i.e., the activities) within an organization.

(2) Operations Research is concerned with making the whole system work with maximum effectiveness and least cost.

(3) OR is a flexible and powerful tool to management in improving their operations.

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Example:

The Two Mines Company own two different mines that produce an ore which, after being crushed, is graded into three classes: high, medium and low-grade. The company has contracted to provide a smelting plant with 12 tons of high-grade, 8 tons of medium-grade and 24 tons of low-grade ore per week. The two mines have different operating characteristics as detailed below.

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Mine Cost per day ($'000) Production (tons/day)

High Medium LowX 180 6 3 4Y 160 1 1 6

How many days per week should each mine be operated to fulfill the smelting plant contract?

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The History of Operations Research

World War II marked the beginning of Operations Research as an organized research. Britain was the first to utilize OR because they already had an OR organization in existence. OR finally crossed the Atlantic to the America’s a few months later as both the Army Air Forces and the Navy began work to analyze different war time situations.

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Because of the war effort, there war an urgent need to allocate scarce resources to the various military operations and to the activities within each operation in an effective manner. Therefore, scientists were asked to do research on (military) operations.

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Characteristics of OR Broad Viewpoint: To resolve the conflicts of interest among the

components of the organization in a way that is best for the organization as a whole.

Search for optimality: Research on the operations of the whole organization to determine the problem and then optimize the operations to improve the organization.

Design and use experimental operations that give an insight into behavior of actual operations.

Team approach: Use of integrated and creative multi-disciplinary team research to solve complex operational problems.

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An OR team (in some companies this may be a single individual) consists of trained researchers that incorporate their own techniques and methods from their fields to the basics of science.

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1. Recognition of a Need: This phase is defined as the perceptions of

needing some sort of resolution or need for improvement.

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2. Problem Formulation: This phase takes the problem, defines it, and

assigns inputs to be used in the next phase. These inputs are variables, parameters and constraints.

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3. Model Construction: This phase takes the variables, parameters and

constraints and constructs a mathematical representation of the problem defined in phase 2. The purpose of this phase is to create the best model so that the variables can be changed and observed.

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4. Data Collection: This phase utilizes the model and the different inputs to the model, which reflect actual problem conditions. Data that is hard to collect include: preferences, opinions, and quality. These items are known as soft data.

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5. Model Solution: This phase actually utilizes the input data and

mathematical algorithms to produce results.

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6. Model Validation and Analysis: This phase is a self-checking phase. It makes

sure that the first four phases are free of errors and that the model accurately represents the problem hand. If there are errors in any of the processes, phase 2 to phase 5 must be redone.

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7. Interpretation of Results: This phase is concerned with examining the

results and makes sure that the solution is the optimum or best solution. Tradeoffs can occur and this is known as sub-optimization.

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8. Decision Making and Implementation: Once a project reaches this phase, the OR is done and

a decision must be made. The outcome of the decision may not directly be related to the results. Other existing external factors play a part in the decision process. These factors can be personal, ethical or political. Whatever the reason, the OR process has been accomplished and this gives management another tool for making a decision on the problem.

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Tools of Operations Research

Linear Programming: Problems involving the allocation of scarce resources such as materials, manpower, machine time or space. Extensively used in problems of blending ingredients, scheduling, manpower planning and economic planning.

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Integer Programming: This is a special case of Linear Programming. This involves problems of resource allocation with the restriction that certain resources are only available in fixed-size units, which can’t be split up. Also used in problems of route selection and other problems involving 0-1 variables.

Integer Programming

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Simulation

Simulation: Problems that involve uncertainty in the system – e.g. in production lines, shops, transport services, manpower modeling. This model is to mimic real life systems and used to evaluate the real system.

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Simulation Of the analytic methods that comprise operations research, simulation stands

in sharp contrast to the mathematical programming algorithms and stochastic models. With simulation, the analyst creates a model of a system that describes some process involving individual entities such as persons, products or messages. The components of the model try to reproduce, with varying degrees of accuracy, the actual operations of the real components of the process. Most likely the system will have time-varying inputs and time-varying outputs that are affected by random events. The components of the simulation are interconnected and can often be viewed as a network with complex input-output relationships. Moreover, the flow of entities through the system is controlled by logic rules that derive from the operating rules and policies associated with the process being modeled. A skilled programmer can duplicate with a high level of accuracy, most systems that can be observed and rationalized. Because of this capacity for detail, simulation has become a very popular method of analysis. Particularly appealing is its ability to model random variables with arbitrary probability distributions and systems that have a variety of interacting random processes. Modern simulation languages are very powerful tools, allowing even a beginner to create representations of complex systems.

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Decision Analysis

Decision Analysis: Problems involving a decision or a series with a small number of options and a small number of outcomes. Examples include decisions on whether or not to test market new products, bidding strategies for contracts and diagnosis of medical condition.

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Queuing Theory

Queuing Theory: Problems where customers are queuing for service of some sort. Examples include shops, banks, telephone exchange, repair of machines, and job-shop scheduling.

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Queuing TheoryThis considers situations that can be modeled as

single queuing stations or networks of queues. For the single queuing station having one or more servers, a variety of analytical results are available when the arrival and service processes are Markovian. Formulas are available to compute statistical estimates for such measures as the average number in the queue, the average waiting time for a customer, and the probability that the service mechanism is busy. Some results are also available for models that are not Markovian. When several queuing stations are interconnected, we have a network of queues. Many decision situations arise in this context.

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Dynamic Programming

Dynamic Programming: Problems involving a series of similar linked decisions, differing only in time or space, such as the choice of the shortest route between two points or decisions involving monthly production or storage.

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TABLE OF CONTENTS

CHAPTER 1 Introduction of ORCHAPTER 2 OR Modeling ResearchCHAPTER 3 Linear Programming CHAPTER 4 Simplex MethodCHAPETR 5 Theory SMCHAPTER 6 Duality theory and SensitivityCHAPTER 7 Other AlgorithmsCHAPTER 8 Transportation and

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TABLE OF CONTENTS

CHAPTER 12 Integer ProgrammingCHAPTER 13 Nonlinear programmingCHAPTER 14 Game Theory CHAPTER 17 Queuing TheoryCHAPTER 18 Inventory TheoryCHAPTER 22 Simulation

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