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MB 0048

Operations Research

Contents

Unit 1

Introduction to OR 1

Unit 2

Linear Programming 19

Unit 3

Simplex Method 46

Unit 4

Duality in L.P.P 75

Unit 5

Transportation Problem 93Unit 6

Assignment Problem 116Unit 7

Integer Programming Problem 136

Unit 8

Infinite Queuing Models 152Edition: Spring 2010

BKID

B1137 7th Jan. 2010

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Unit 9

Finite Queuing Models 180

Unit 10

Simulation 191

Unit 11

Project Scheduling and PERT-CPM 215

Unit 12

Game Theory 234

References 253

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DeanDirectorate of Distance EducationSikkim Manipal University

Board of Studies

Chairman Mr. Pankaj KhannaHOD Management & Commerce DirectorSMU DDE HR, Fidelity Mutual Fund

Additional Registrar Mr. Shankar JagannathanSMU DDE Former Group Treasurer

Wipro Technologies Limited

Controller of Examination Mr. Abraham MathewSMU DDE Chief Financial Officer

Infosys BPO, Bangalore

Dr. T. V. Narasimha Rao Ms. Sadhna Dash

Adjunct Faculty & Advisor Ex-Senior Manager, HRSMU DDE Microsoft India Corporation (Pvt.) Ltd.

Prof. K. V. VaramballyDirectorManipal Institute of ManagementManipal

Content Preparation Team Content Editing Peer Review ByProf. S. Santhanam Mr. Subhabaha Pal Prof. K. C. S. Rao(Faculty M P Birla Institute Lecturer, SMU DDE Chairman, MBA (BT)of Management) Bangalore School of Management

Studies, PondicherryMrs. Sharada Rudramurthy University, Pondicherry

(Visiting Faculty

SIET)

Edition: Spring 2010

This book is a distance education module comprising of collection of learningmaterial for our students.

All rights reserved. No part of this work may be reproduced in any form by anymeans without permission in writing from Sikkim Manipal University of Health,Medical and Technological Sciences, Gangtok, Sikkim.

Printed and Published on behalf of Sikkim Manipal University of Health, Medical andTechnological Sciences, Gangtok, Sikkim by Mr. Rajkumar Mascreen, GM, ManipalUniversal Learning Pvt. Ltd., Manipal 576 104. Printed at Manipal Press Limited,Manipal.

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SUBJECT INTRODUCTION

Operations Research is an important course of study for a management

student. It is a branch of applied mathematics and has diverse applications.This subject essentially deals with problems of choices and optimization of

resource utilization.

This courseware comprises 12 units:

Unit 1: Introduction to OR

This unit provides the definition, scope and limitations of OR.

Unit 2: Linear Programming

This unit explainsLinear programming, which focuses on obtaining the bestpossible output (or a set of outputs) from a given set of limited resources.

Unit 3: Simplex Method

This unit explains the simplex method focuses, which on solving LPP of any

enormity involving two or more decision variables.

Unit 4: Duality in L.P.P

This unit explains the duality in L.P.P.

Unit 5: Transportation Problem

This unit explains transportation model in Operations Research

Management.

Unit 6: Assignment ProblemThis unit explains the assignment problem, which is a special case of the

transportation problem, where the objective is to minimise the cost or time of

completing a number of jobs by a number of persons, maximise revenue

and sales efficiently.

Unit 7: Integer Programming Problem

This unit explains the Integer Programming Problem (IPP), which is a

special case of Linear Programming Problem (LPP), where all or some

variables are constrained to assume non-negative integer values.

Unit 8: Infinite Queuing Models

This unit explains how a queuing model used to approximate a queuing

situation for the queuing method is to be analysed mathematically.

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Unit 9: Finite Queuing Models

This unit describes such scenarios where the possible number of arrivals is

limited and small.

Unit 10: Simulation

This unit explains simulations.

Unit 11: Project Scheduling and PERT-CPM

This unit explains Project Scheduling and PERT-CPM.

Unit 12: Game Theory

This unit explains Games Theory.