Quantitative Techniques for Managerial Decisions

666 Pages·2012·44.232 MB·Englsih

by  R.B. Khanna

QUANTITATIVE TECHNIQUES
FOR
MANAGERIAL DECISIONS
Second Edition
R.B. KHANNA
Professor
Indian Institute for Planning and Management (IIPM)
Jaipur
New Delhi-110001
2012
QUANTITATIVE TECHNIQUES FOR MANAGERIAL DECISIONS, Second Edition
R.B. Khanna
© 2012 by PHI Learning Private Limited, New Delhi. All rights reserved. No part of this book may be
reproduced in any form, by mimeograph or any other means, without permission in writing from the
publisher.
ISBN-978-81-203-4596-6
The export rights of this book are vested solely with the publisher.
Third Printing (Second Edition) … … … June, 2012
Published by Asoke K. Ghosh, PHI Learning Private Limited, M-97, Connaught Circus,
New Delhi-110001 and Printed by Mudrak, 30-A, Patparganj, Delhi-110091.
For those who matter most to me
Saroj, Shashi, Shweta, Dhiraj, Aparna and Roshni
Preface………xi
Preface to the First Edition………xiii
1. Decision Making—A Quantitative Approach………1–20
Learning Objectives………1
The Decision Dilemma………1
1.1 Introduction………2
1.2 Operations Research—The Quantitative Approach to Decision
Making………4
1.3 Definitions of Operations Research………5
1.4 Characteristics of Operations Research………6
1.5 Models and Modelling in OR………7
1.6 OR Methodology………8
1.7 OR Techniques………14
1.8 Typical Applications of Operations Research………16
1.9 OR and Computers………17
1.10 Summary………17
Concept Quiz………17
Questions………20
SECTION A LINEAR PROGRAMMING
2. Linear Programming—Graphic Method………23–63
Learning Objectives………23
Crisis at Bhilpur………23
2.1 Introduction………24
2.2 Basic Requirements of a Linear Programming Problem………25
2.3 Graphical Solution to a Maximisation Problem………26
2.4 Summary of Graphical Maximisation Procedure………29
2.5 Technical Issues in Linear Programming………30
2.6 Minimisation Problem………32
2.7 Solution by Computer Package………34
2.8 Problem Formulation………36
2.9 Basic Assumptions of Linear Programming………51
2.10 Advantages and Limitations of Linear Programming………52
2.11 Summary………53
Concept Quiz………53
Questions 56
3. Linear Programming—Simplex Method………64–136
Learning Objectives………64
Manthan 64
3.1 Introduction………65
3.2 Setting up the Initial Solution ………66
3.3 Developing the Second Solution………69
3.4 Developing the Third Solution………73
3.5 Developing the Fourth Solution ………74
3.6 Summary of Steps in the Simplex Maximisation Procedure………76
3.7 Simplex Solution to a Minimisation Problem………76
3.8 Developing the Second Solution………79
3.9 Developing the Third Solution………80
3.10 Dual………82
3.11 Sensitivity Analysis………87
3.12 Solution by Computer Package………91
3.13 Technical Issues in the Simplex Method………95
3.14 Two Phase Method of Solving Problems Involving Artificial
Variables………100
3.15 Solved Examples………102
3.16 Summary………121
Concept Quiz………122
Questions………124
SECTION B STOCHASTIC TECHNIQUES
4. Probability………139–171
Learning Objectives………139
Oil or Gas 139
4.1 Introduction………139
4.2 Basic Probability Concepts………140
4.3 Approaches to Probability………141
4.4 Addition Rules………143
4.5 Probabilities under Conditions of Statistical
Independence………147
4.6 Probabilities under Conditions of Statistical Dependence………151
4.7 Revising Prior Estimates of Priorities: Baye’s Theorem………155
4.8 Solved Examples………157
4.9 Summary………164
Concept Quiz………165
Questions………168
5. Probability Distributions………172–197
Learning Objectives………172
Vahan Ancillaries………172
5.1 Introduction………173
5.2 Types of Probability Distributions………174
5.3 Random Variable………174
5.4 Expected Value of a Random Variable………174
5.5 Mean of a Distribution………176
5.6 Standard Deviation of a Distribution………176
5.7 Binomial Distribution………177
5.8 Poisson Distribution………178
5.9 Normal Distribution………179
5.10 Application Areas of Probability and Probability
Distributions………186
5.11 Solved Examples………187
5.12 Summary………191
Concept Quiz………193
Questions………195
6. Decision Theory………198–241
Learning Objectives………198
On Oily Waters………198
6.1 Introduction ………199
6.2 Steps in Decision Making………201
6.3 Decision Making Environment………202
6.4 Decision Making under Uncertainty………202
6.5 Decision Making under Risk………205
6.6 Expected Value of Perfect Information (EVPI)………208
6.7 An Alternative Approach—Minimising Expected Losses………209
6.8 Marginal Analysis………210
6.9 Utility as a Decision Criterion………211
6.10 Decision Trees………214
6.11 Expected Value of Sample Information (EVSI)………217
6.12 Bayesian Revision of Probabilities………217
6.13 Solution by Computer Package………220
6.14 Solved Examples………223
6.15 Summary………230
Concept Quiz………232
Questions………234
7. Theory of Games………242–268
Learning Objectives………242
Blue Scooters Limited………242
7.1 Introduction………243
7.2 Assumptions, Definitions and Classification of Games ………243
7.3 Two-Person Zero Sum Games………244
7.4 Pure Strategies and Saddle Points………245
7.5 Mixed Strategies………246
7.6 Shortcut Method for Finding Optimum Mixed Strategies………248
7.7 Solution of Games by Dominance………249
7.8 Graphical Solution of Games………252
7.9 Solution by Linear Programming………257
7.10 Solved Examples………259
7.11 Solution by Computer Package………262
7.12 Summary………263
Concept Quiz………263
Questions………265
SECTION C MATHEMATICS FOR MANAGERS
8. Matrix Algebra………271–310
Learning Objectives………271
8.1 Introduction………271
8.2 Definitions………272
8.3 Operations on Matrices………273
8.4 Determinants………278
8.5 Inverse of a Matrix………281
8.6 Solution of a Set of n Simultaneous Linear Equations in
n Variables………282
8.7 Applications………288
8.8 Solved Examples………293
8.9 Summary………303
Concept Quiz………304
Questions………306
9. Differential Calculus………311–333
Learning Objectives………311
9.1 Introduction………311
9.2 Functions and Limits………312
9.3 Concept of Slope and Rate of Change………313
9.4 Rules of Differentiation………314
9.5 Higher Order Derivatives………317
9.6 Applications………317
9.7 Solved Examples………321
9.8 Summary………328
Concept Quiz………329
Questions………331
10. Regression and Correlation………334–359
Learning Objectives………334
10.1 Introduction………334
10.2 Simple Linear Regression………335
10.3 Correlation………339
10.4 Karl Pearson’s Coefficient of Linear Correlation………341
10.5 Spearman’s Rank Correlation………343
10.6 Solved Examples………345
10.7 Summary………353
Concept Quiz………354
Questions………356
SECTION D EXTENSIONS OF LINEAR PROGRAMMING
11. Transportation Model………363–430
Learning Objectives………363
Ashiana………363
11.1 Introduction………364
11.2 Setting up the Transportation Tableau………364
11.3 Testing the Solution for Improvement………374
11.4 The Unbalanced Case (Demand and Supply are Unequal)
………384
11.5 Multiple Solutions………386
11.6 Degeneracy………387
11.7 Maximisation Problems………389
11.8 Least Time Transportation Model………391
11.9 Transhipment Model………394
11.10 Restrictions on Routes………395
11.11 Solution by Computer Package………395
11.12 Solved Examples………398
11.13 Summary ………414
Concept Quiz………414
Questions………417
12. Assignment Model………431–476
Learning Objectives………431
Mettalica Works Limited………431
12.1 Introduction………432
12.2 The Hungarian Method………433
12.3 Summary of the Assignment Method………437
12.4 Maximisation Case………437
12.5 Travelling Salesman Problem………440
12.6 Solution by Computer Package………443
12.7 Solved Examples………445
12.8 Summary………464
Concept Quiz………465
Questions………468
SECTION E PRECEDENCE MODELS
13. Network Models—CPM and PERT………479–541
Learning Objectives……… 479
Rasoi Appliances……… 479
13.1 Introduction……… 480
13.2 Critical Path Method (CPM)………481
13.3 Definitions………482
13.4 Rules and Conventions………482
13.5 Drawing a Network [Activity on Arrow (AOA)]………483
13.6 Calculating Earliest Start Time………485
13.7 Calculating Latest Finish Time (LFT)………486
13.8 Floats (Slacks), Critical Activities and Critical Path………487
13.9 Activity on Node (AON) Network………490
13.10 Crashing a Project………495
13.11 Resource Levelling………500
13.12 Control of Project Costs………502
13.13 Programme Evaluation and Review Technique (PERT)………504