Decision Theory: An Introduction to Dynamic Programming and Sequential Decisions(Wiley Interscience Series in Systems and Optimization)

Decision Theory An Introduction to Dynamic Programming and Sequential Decisions John Bather University of Sussex, UK Mathematical induction, and its use in solving optimization problems, is a topic of great interest with many applications. It enables us to study multistage decision problems by proceeding backwards in time, using a method called dynamic programming. All the techniques needed to solve the various problems are explained, and the author's fluent style will leave the reader with an avid interest in the subject. * Tailored to the needs of students of optimization and decision theory * Written in a lucid style with numerous examples and applications * Coverage of deterministic models: maximizing utilities, directed networks, shortest paths, critical path analysis, scheduling and convexity * Coverage of stochastic models: stochastic dynamic programming, optimal stopping problems and other special topics * Coverage of advanced topics: Markov decision processes, minimizing expected costs, policy improvements and problems with unknown statistical parameters * Contains exercises at the end of each chapter, with hints in an appendix Aimed primarily at students of mathematics and statistics, the lucid text will also appeal to engineering and science students and those working in the areas of optimization and operations research.

Table of Contents:
Preface xi 1 Introduction 1 1.1 Mathematical Induction 1 1.2 Historical Background 2 1.3 Dynamic Programming 5 1.4 The Executioner’s Tale 8 1.5 Summary 8 Exercises 10 I Deterministic Models 11 2 Multi-Stage Decision Problems 13 2.1 Maximizing Utilities 13 2.2 A General Model 17 2.3 Applications 19 Exercises 25 3 Networks 27 3.1 Shortest Paths 27 3.2 Directed Networks 29 3.3 Critical Path Analysis 30 Exercises 37 4 Further Applications 39 4.1 Discrete Actions 39 4.2 The Knapsack Problem 39 4.3 A Simple Replacement Model 42 4.4 Scheduling Problems 44 4.5 Johnson’s Algorithm 45 Exercises 49 5 Convexity 51 5.1 Convex and Concave Functions 51 5.2 Allocation Problems 56 5.3 Concave Utility Functions 60 Exercises 64 II Stochastic Models 67 6 Markov Systems 69 6.1 Introduction 69 6.2 Stochastic Dynamic Programming 70 6.3 Applications 72 Exercises 78 7 Optimal Stopping 79 7.1 Introduction 79 7.2 Stopping Times and Stopping Sets 82 7.3 Applications 90 Exercises 94 8 Special Problems 97 8.1 Introduction 97 8.2 Selling an Asset 97 8.3 The Marriage Problem 104 8.4 Prophet Inequalities 109 Exercises 116 III Markov Decision Processes 119 9 General Theory 121 9.1 Introduction 121 9.2 Minimizing Discounted Expectations 122 9.3 Policy Improvements 130 9.4 A Machine Replacement Model 137 10 Minimizing Average Costs 145 10.1 Introduction 145 10.2 Long-Term Average Costs 148 10.3 Extension to Infinitely Many States 153 10.4 Optimal Inventory Policies 158 11 Statistical Decisions 165 11.1 Introduction 165 11.2 Testing Statistical Hypotheses 166 11.3 The Sequential Probability Ratio Test 170 Notes On the Exercises 177 Chapter 1 177 Chapter 2 177 Chapter 3 178 Chapter 4 179 Chapter 5 179 Chapter 6 180 Chapter 7 181 Chapter 8 183 References 185 Index 187

About the Author :
John Bather is the author of Decision Theory: An Introduction to Dynamic Programming and Sequential Decisions, published by Wiley.

Review :
"This textbook...draws on his many years of experience in teaching this topic as well as on his considerable professional expertise in the area. It is ideally suited to its stated purpose as a student text." (Short Book Reviews, Vol. 20. No. 3, December 2000) "...I was impressed with this book..." (The Statistician, Vol.51, No.2 2002) "...excellent for the audience to whom it is addressed, and it is to be hoped that the author will write a further textbook..." (Jnl of the Operational Research Society, Vol 54(10) 2003)