Operations Research By Dr. Qazi Shoeb Ahmad, Dr. Shakeel Javed, Dr.Mohd. Vaseem Ismail

Operations Research By Dr. Qazi Shoeb Ahmad, Dr. Shakeel Javed, Dr.Mohd. Vaseem Ismail
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Operations Research By Dr. Qazi Shoeb Ahmad, Dr. Shakeel Javed, Dr.Mohd. Vaseem Ismail

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Publisher: Laxmi Publications
ISBN: 9789381159651
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Preface
T
he authors feel great pleasure in presenting the first edition of the book Operations Research . This book is designed to meet the requirement of B.Tech, M.B.A., B.B.A. students of different Universities.
The subject matter has been discussed in such a way that the students will find no difficulty to understand it. Each chapter of this book contains complete self-explanatory theory and a large number of solved examples, followed by a collection of good exercises. The language of the book is simple and easy to understand. The authors hope that the students, teachers and other readers will find the book interesting and to the point covering the whole course. We hope that the students will receive the book warmly. We have taken great care in eliminating the misprints, but if there are still any, we shall be highly obliged to those who will take trouble of pointing them out. Suggestions for the improvement of the book will be gratefully acknowledged. Authors
ix
UNIT I LINEAR PROGRAMMING
CHAPTER
1
Graphical Solution and Formulation 1.1 LINEAR PROGRAMMING Linear programming deals with the maximization or minimization or optimization of a function of variables known as objective function, subject to a set of linear equalities and or inequalities known as constraints. Here, the objective function can be cost, profit or production capacity, which is to be obtained in the best possible manner. The constraints may be imposed by different sources such as market demand, storage capacity, raw material availability etc. The word linear here implies that the variables, considered here do not certain any powers greater than one. Thus, a given change in one variable will always cause a resulting proportional change in another variable. The word programming refers to modelling and solving a problem mathematically that involves the economic allocation of limited resources by choosing a particular course of action or a strategy among various alternative strategies to achieve the desired objective. G.B. Dantzig developed the technique primarily for solving military logistics problems. But nowadays, it is being used widely in all the areas of management, education, transportation planning, military operations, healthcare systems, education etc.
1.2 STRUCTURE OF LINEAR PROGRAMMING MODEL The general structure of LP model consists of mainly three basic components a Decision variables. The Operation Researcher needs to evaluate various alternatives or courses of action for arriving at the optimal value of the objective function. If there is no alternative to be selection among various alternatives, then there is no need of linear programming. The evaluation of various alternatives can be obtained by the nature of