Introduction to Management Science: Modelling, Optimisation and Probability

Abstract

Businesses have to cut costs, increase revenue and be profitable. The aim of this book is to introduce Management Science to analyse business challenges and to find solutions analytically. Important topics in modelling, optimisation and probability are covered. These include: linear and integer programming, network flows and transportation; essential statistics, queueing systems and inventory models. The overall objectives are: to enable the reader to increase the efficiency and productivity of businesses; to observe and define challenges in a concise, precise and logical manner; to be familiar with a number of classical and state-of-the art operational research techniques and tools; to devise solutions, algorithms and methods that offer competitive advantage to businesses and organisations; and to provide results to management for decision making and implementation. Numerous examples and problems with solutions are given to demonstrate how these concepts can be applied in a business context.

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Contents
IModelling
1Introduction ................................. 3
1.1 Aim and Objectives 3
1.2 Grand Example 4
1.3 Disciplines 7
1.4 Structure 8
2Modelling ................................... 9
2.1 Introduction 9
2.2 The Analysis Process 10
2.3 Break-Even Analysis 13
2.4 Techniques and Applications 15
2.5 Computer Lab – Modelling 18

2.6 Problems 27
2.7 Summary 27
2.8 Annotated Bibliography 28
II Optimisations
3Mathematical Programming . . . . . . . . . . . . . . . . 31
3.1 Introduction 31
3.2 Problem Formulation 32
3.3 Mathematical Model 33
3.4 Feasible and Infeasible Regions 35
3.5 Optimal Solution 36
3.6 Applications 38
3.7 Computer Lab – Optimisations 43
3.8 Problems 48
3.9 Summary 50
3.10 Annotated Bibliography 50
4Transportation Models ...................... 53
4.1 Introduction 53
4.2 Transportation Model 54
4.2.1 Data Collection ............................... 55
4.2.2 Network Model ............................... 56
4.2.3 Linear Program ................................ 58
4.2.4 Feasible and Optimal Solution .................... 59
4.3 Transshipment Model 60
4.4 Assignment Model 66
4.5 Applications and Examples 72
4.6 Computer Lab – Transportation 72
4.7 Problems 76
4.8 Summary 80
4.9 Annotated Bibliography 81

5Network Flows .............................. 83
5.1 Introduction 83
5.2 Graph Theory 84
5.3 Minimum Spanning Tree 86
5.3.1 Examples .................................... 86
5.3.2 Kruskal’s Algorithm ............................. 90
5.3.3 Applications .................................. 92
5.4 Shortest Path 94
5.4.1 Example ..................................... 95
5.4.2 Dijkstra’s Algorithm .............................101
5.4.3 0-1 Program ..................................103
5.4.4 Applications ..................................104
5.5 Maximum Flow 106
5.5.1 Example .....................................107
5.5.2 Algorithm ....................................109
5.5.3 Integer Program ...............................111
5.5.4 Applications ..................................112
5.6 Computer Lab – SP & MF 113
5.7 Problems 120
5.8 Summary 125
5.9 Annotated Bibliography 126
III Probabilistic Approaches
6Probability and Statistics . . . . . . . . . . . . . . . . . . . 131
6.1 Introduction 131
6.2 Probability 132
6.2.1 Fundamentals ................................132
6.2.2 Binomial Distribution ............................137
6.2.3 Joint, Conditional and Marginal Probabilities . . . . . . . . 141
6.2.4 Bayesian Networks .............................145
6.3 Expectation and Standard Deviation 148
6.3.1 Expectation ..................................148
6.3.2 Standard Deviation ............................150

6.4 Normal Distribution 154
6.5 Computer Lab – Probabilities 159
6.6 Problems 165
6.7 Summary 166
6.8 Annotated Bibliography 167
7Queueing Systems . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.1 Introduction 169
7.2 Fundamentals 171
7.2.1 Terminology ..................................171
7.2.2 Characteristics ................................174
7.3 Single Server System 176
7.3.1 Birth-Death Process ............................176
7.3.2 Probabilities ..................................177
7.3.3 Customers in System ...........................180
7.3.4 Little’s Law ...................................182
7.3.5 Operational Characteristics . . . . . . . . . . . . . . . . . . . . . 183
7.4 Multiple Server System 185
7.5 Computer Lab – Queueing Systems 190
7.6 Problems 194
7.7 Summary 197
7.8 Annotated Bibliography 198
8Inventory Models . . . . . . . . . . . . . . . . . . . . . . . . . 199
8.1 Introduction 199
8.2 Inventory Management 200
8.2.1 Role, Types and Predictions ......................200
8.2.2 Definitions, Classification and Costs . . . . . . . . . . . . . . . . 203
8.3 Economic Order Quantity Models 207
8.3.1 Basic Economic Order Quantity Model . . . . . . . . . . . . . 207
8.3.2 Production Lot Size Model . . . . . . . . . . . . . . . . . . . . . . . 211
8.3.3 Shortage Model ...............................215
8.4 Reorder Point Models 219
8.5 Computer Lab – EOQ 224
8.6 Problems 227

8.7 Summary 229
8.8 Annotated Bibliography 230
IV Final Part
Solutions to Problems . . . . . . . . . . . . . . . . . . . . . . 233
Appendix ................................. 265
References ................................ 269
Index ..................................... 273