A COMPUTERIZED APPROACH TO SOLVING OPERATION RESEARCH PROBLEMS USING LINEAR PROGRAMMING TECHNIQUES

CHAPTER ONE

INTRODUCTION

1.1 Background to the Study

Now a day Operations research has been applying by every large organization in developed nation and developing country in every department at all level. Availability of faster and flexible computing facilities and the number of qualified OR professionals have enhanced the acceptance and popularity of the discipline. In the country like USA and the UK growth of OR has not been limited, now it has reached to many countries including India.

The main idea of operation research-based modelling in computer science applications is the systematic approach to deal with the problem and get the optimized solution. This is one of the best platforms where we get the best knowledge through profit and loss concept. This study is aimed to find the minimum cost and expected time to finish a project. Operation Research also represents a clear idea about co-operation between intelligent relations with decision making. The optimization models are very useful in computer science, especially in software engineering and computer network domains. A system model can be built and mathematically prove by O.R models. The main overview of Operation Research is to give the perfect solutions to win a war without fighting it. The implementation of O.R. is mainly depended on the person who provides the solution and the person who use the solutions. In this paper, we try to discuss and find the research directions of optimization models in computer science domains.

Operational research encompasses a wide range of problem-solving techniques and methods applied in the detection of improved decision-making and efficiency Leachman et al (2013). Some of the tools used by operational researchers are statistics, optimization, probability theory, queuing theory, game theory, graph theory, decision analysis, mathematical modeling and simulation. Because of the computational nature of these fields, OR also has strong ties to science.

Application work in operational research, like other engineering and economics’ disciplines, attempts to use models to make a practical impact on real-world problems.

1.2 Statement of the Problem

Linear programs can provide reasonably realistic representations of many real-world problems especially if a little creativity is applied in the mathematical formulation of the problem. In spite of the overwhelming number of real life applications, linear programming techniques do have some limitations. These are highlighted below: Linear programming is based on a set of rather restrictive assumptions. Although these assumptions will be valid for many practical problems, there are numerous other situations in which one or more of the suppositions may not be factual. Some of the limitations associated with linear programming technique include the following (i) indivisibility (ii) multiple objectives (iii) Uncertainty (iv) Non Linear relationships and (v) sequential problems. Some of these limitations are briefly discussed below Indivisibility:

The linear programming model (assumes that each decision variable is divisible into fractional value. Such assumption generally will be valid when these variables a physical measure (Weight, capacity, length, area or volume), time, monetary values or percentages. Linear programming may not provide such whole –unit or integer solutions. For example, a solution may result in 3.56 chairs which is not practical since discrete solution is desirable. The proper tool to use for such an analysis is the integer programming model. Multiple Objectives: The linear programming model also assumes that there is only a single objective in the problem. Furthermore, it is presumed that the objective can be expressed in terms of a numerical criterion such as quantity, time or revenue. However, an objective could be expressed in terms of different criterion and may not be possible to quantify. For instance, it is hard to measure social benefits, customer satisfaction, quality and similar criteria in numerical terms. These objectives/ goals may be equal in dimension, complimentary or even conflicting. The appropriate tool to use in such a situation is the goal programming model Uncertainty: The assumption of certainty has its limitation in that some situations occur where factors like costs and other constrain requirements may not be known before hand. In such a situation, probabilistic linear programming technique is more applicable. The Non Linear Relationships: As a result of expansion and contraction, decision variable constraint utilization rate may fluctuate, rather than remain constant as the level of activity changes. In addition, each decision does not always make a constant and independent contribution to the objective. Furthermore, decision variables frequently have interrelated, rather than independent effects on the criterion value. In such situations, the appropriate tool to use is the non linear programming techniques. Sequential Problems: The linear programming model assumes that a problem involves single, one-time decision making. In real life situation, it is not always so as most problems involve a series of interrelated decisions.

1.3 Aim/Objectives Of Study

The main objectives of this thesis is to develop a computerized model in  solving Operation Research Problems using Linear programming Techniques.

1.4 Significance of the Study

This research will be a contribution to the body of literature in the area of the effect of personality trait on student’s academic performance, thereby constituting the empirical literature for future research in the subject area

1.5 Basic Assumptions

If the new design is completely implemented the whole problems associated with the existing system will be all solved.

1.6 LIMITATION OF STUDY

Financial constraint– Insufficient fund tends to impede the efficiency of the researcher in sourcing for the relevant materials, literature or information and in the process of data collection (internet, questionnaire and interview).

Time constraint– The researcher will simultaneously engage in this study with other academic work. This consequently will cut down on the time devoted for the research work

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