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Op"erations

Research

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intentionally left blank Copyright © 2007, 2005 New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers

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ISBN (13) : 978-81-224-2944-2

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PREFACE

I started my teaching career in the year 1964. I was teaching Productio n Engineering subjects till

1972. In the year 1972 I have registered my name for the Industrial Engi

neering examination at National

Institution of Industrial Engineering, Bombay. Since then, I have shifted my field for interest to Industrial

Engineering subjects and started teaching related subjects. One such sub ject is OPERATIONS RESEARCH. After teaching these subjects till my retirement in the year 2

002, it is my responsibility to

help the students with a book on Operations research. The first volume o f the book is LINEAR PORGRAMMING MODELS. This was published in the year 2003. Now I am giving this book OPERATIONS RESEARCH, with other chapters to students, with a hope that it wil l help them to understand the subject easily. I hope this will help my teacher friends to teach the subject well. I thank Mr. N.V. Jagdeesh Babu, Assistant professor of Mechanical Engineering for proof reading the script.

Anantapur

Date: 12.1.2007P. Rama Murthy.

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Dedicated To

My Wife Usha

My Daughter Vidya

Grandson Yagnavalkya.

and My Son In Law Shankaranarayana

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CONTENTS

Preface

ChapterTitle Page number

1. Historical Development........................................................................

....1-21

2. Linear Programming models (Resource

allocation models) ................. 22-43

3. Linear Programming models (Solution by Simplex method).............. 44-140

4. Linear Programming - II

(Transportation Problem)..........................141-211

5. Linear Programming III (Assignment Model).................................. 212-254

6. Sequencing Model ........................................................................

..... 255-294

7. Replacement Model........................................................................

... 295-353

8. Inventory Control........................................................................

...... 354-445

9. Waiting line theory or Queuing Model............................................... 446-484

10. Theory of Games or Competitive Strategies..................................... 485-563

11. Dynamic Programming .....................................................................564-592

12. Decision Theory ........................................................................

........ 593-616

13. Simulation........................................................................

.................. 617-626

14. Introduction to Non - Linear Programming...................................... 627-634

15. Programme Evaluation and Review Technique and

Critical Path Method (PERT AND CPM).......................................... 635-670

Multiple choice question and answers .......................................................... 671-702

Index ........................................................................ ................................... 703-705

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1.1. INTRODUCTION

The subject OPERATIONS RESEARCH is a branch of mathematics - specially applied mathematics, used to provide a scientific base for management to take timely and effe ctive decisions to their problems. It tries to avoid the dangers from taking decisions merely by guessing o r by using thumb rules. Management is the multidimensional and dynamic concept. It is multidimen sional, because management problems and their solutions have consequences in several dimensions, su ch as human, economic social and political fields. As the manager operates his system in an en vironment, which will never remain static, hence is dynamic in nature. Hence any manager, while making decisions, consider all aspects in addition to economic aspect, so that his solution should be u seful in all aspects. The general approach is to analyse the problem in economic terms and then implement the solution if it does not aggressive or violent to other aspects like human, social and politi cal constraints. Management may be considered as the process of integrating the efforts o f a purposeful group, or organisation, whose members have at least one common goal. You have studied various schools of management in your management science. Most important among them which u ses scientific basis for decision making are: (i) The Decision theory or Decisional Management School and (ii) The Mathematical or Quantitative Measurement School. The above-mentioned schools of management thought advocate the use of mathematical methods or quantitative methods for making decisions. Quantitative approach to management problems requ ires that decision problems be defined, analyzed, and solved in a conscious, rational, logical and systematic and scientific manner - based on data, facts, information and logic, and not on mere guess work or thumb rules. Here we use objectively measured decision criteria. Operati ons research is the body of knowledge, which uses mathematical techniques to solve management proble ms and make timely optimal decisions. Operations Research is concerned with helping manager s and executives to make better decisions. Today's manager is working in a highly competitive and dynamic environment. In present environment, the manager has to deal with systems with complex i nterrelationship of various factors among them as well as equally complicated dependence of the crit erion of effective performance of the system on these factors, conventional methods of decision-making is found very much inadequate. Though the common sense, experience, and commitment of the manager is es sential in making decision, we cannot deny the role-played by scientific methods in making optimal d ecisions. Operations Research

CHAPTER - 1

Historical Development

22222Operations Research

uses logical analysis and analytical techniques to study the behaviour o f a system in relation to its overall working as resulting from its functionally interconnected constr aints, whose parameters are recognized, quantified wherever possible relationships identified to the extent possible and alterative decisions are derived. Conventional managers were very much worried about that an Operations Re search analyst replace them as a decision maker, but immediately they could appreciated him due to his mathematical and logical knowledge, which he applies while making decisions. But oper ations research analyst list

out alternative solutions and their consequences to ease manager's work of decision making. Operations

research gives rationality to decision-making with clear view of possibl e consequences. The scope of quantitative methods is very broad. They are applied in def ining the problems and getting solutions of various organisatons like, business, Government org anisations, profit making units and non-profit units and service units. They can be applied to variety o f problems like deciding plant location, Inventory control, Replacement problems, Production scheduling , return on investment analysis (ROI), Portfolio selection, marketing research and so on. This book, d eals with basic models of Operations research and quantitative methods. The students have to go th rough advanced Operations Research books, to understand the scope of the subject. Two important aspects of quantitative methods are: (a) Availability of well-structured models and methods in solving the problem s, (b) The attitude of search, conducted on a scientific basis, for increased k nowledge in the management of organisations. Therefore, the attitude encompassed in the quantitative approaches is pe rhaps more important than the specific methods or techniques. It is only by adopting this att itude that the boundaries and application of the quantitative approach can be advanced to include thos e areas where, at first glance, quantitative data and facts are hard to come by. Hence, quantitative approach has found place in

traditional business and as well in social problems, public policy, national, international problems and

interpersonal problems. In fact we can say that the application of quant itative techniques is not limited to any area and can be conveniently applied to all walks of life as far as decision-making is concerned. The quantitative approach does not preclude the qualitative or judgement al elements that almost always exert a substantial influence on managerial decision-makin g. Quite the contrary. In actual practice, the quantitative approach must build upon, be modified by, and continually benefit from the experiences and creative insight of business managers. In fact quantitative approach imposes a special responsibility on the manager. It makes modern manager to cultivate a managerial style that demand conscious, systematic and scientific analys is - and resolution - of decision problems. In real world problems, we can notice that there exists a relationship a mong intuition, judgement, science, quantitative attitudes, practices, methods and models, as shown in figure 1.1. The figure depicts that higher the degree of complexity and the degree o f turbulence in the environment, the greater is the importance of the qualitative approach t o management. On the other

hand, the lower the degree of complexity i.e., simple and well-structured problems, and lesser degree

of turbulence in the environment, the greater is the potential of quanti tative models. The advancement in quantitative approach to management problems is due to two facts. The y are: (a) Research efforts have been and are being directed to discover and develo p more efficient tools and techniques to solve decision problems of all types.

Historical Development33333

(b) Through a continuous process of testing new frontiers, attempts have bee n made to expand the boundaries and application potential of the available techniques. Quantitative approach is assuming an increasing degree of importance in the theory and practice of management because of the following reasons. (a) Decision problems of modern management are so complex that only a consci ous, systematic and scientifically based analysis can yield a realistic fruitful solutio n. (b) Availability of list of more potential models in solving complex manageri al problems. (c) The most important one is that availability of high speed computers to s olve large and complex real world problems in less time and at least cost and which hel p the managers to take timely decision. One thing we have to remember here is that if managers are to fully util ize the potentials of management science models and computers, then problems will have to be s tated in quantitative terms.

As far as the title of the subject is concerned, the terms ‘quantitative approach", ‘operations

research", ‘management science", ‘systems analysis" and ‘ systems science" are often used interchangeably. What ever be the name of the subject, the syllabi and subject matter d ealt which willquotesdbs_dbs14.pdfusesText_20

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