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Dynamic programming

Author: White, D. J. Series: Mathematical economic texts ; 1 Publisher: Oliver and Boyd, 1969. ; Holden Day, 1969.Language: EnglishDescription: 180 p. ; 24 cm.ISBN: 1050016245Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA402.5 .W45 1969
(Browse shelf)
001193436
Available 001193436
Total holds: 0

Includes bibliographical references and index

Digitized

Dynamic Programming Contents ACKNOWLEDGEMENTS CHAPTER 1 INTRODUCTION CHAPTER 2 THE OPTIMAL PATH PROBLEM 2.1 Statement of Problem 2.2 Derivation of the Functional Equation 2.3 Computational Algorithms A. Method of Successive Approximations B. Method of Approximation in Policy Space C. Direct Method for Directed Sets 2.4 Some Advantages of Dynamic Programming for the Optimal Path Problem 2.5 Example 2.6 Some Interpretations of the Optimal Path Problem ix 1 7 7 7 8 8 10 10 10 11 15 CHAPTER 3 THE NATURE OF DYNAMIC PROGRAMMING 3.1 Sequentially Controlled Systems 3.2 Variations in the Nature of Sequentially Controlled Systems 3.3 Dynamic Programming, Functional Equations and the Principle of Optimality 3.4 Dynamic Programming and Classical Optimisation Problems 21 21 23 29 32 CHAPTER 4 DETERMINISTIC PROCESSES 4.1 Dynamic Programming and Non-Sequential Discrete Optimisation Problems A. Allocation Problems B. Assortment Problems 4.2 Dynamic Programming and Sequential Discrete Optimisation Problems A. Long Term Planning Problems (a) Optimal Equipment Replacement Policies (b) Optimal Capacity Expansion Policies B. Multi-stage Production Processes (a) Optimal Operation of a Multi-stand Rolling Mill (b) Multi-stage Chemical Processes C. Sequencing Problems 4.3 The Calculus of Variations and Pontryagin's Maximum Principle 4.4 Functional Approximation 37 37 37 43 47 47 48 56 64 64 69 71 74 84 Vi CHAPTER 5 STOCHASTIC PROCESSES CONTENTS 89 5.1 Finite Discrete Markov Processes 90 5.2 An Alternative Computational Algorithm 94 5.3 Processes Involving Full or Partial Choice of Decision Interval 96 5.3.1 A Fixed Action, Completely Controlled Decision Interval, Process 96 (a) A Sequential Inspection Process 96 (b) Optimal Revision Policies 100 5.3.2 A Fixed Action, Partially Controlled Decision Interval, Process 103 5.3.3 A Variable Action, Partially Controlled Decision Interval, Process. A Replacement Problem 104 5.4 Stochastic Constraints. Inventory Control Problems 106 5.5 A Linear Programming Approach 107 5.6 Approximation Using Expectations 108 5.7 Analytic Derivation of Policies. Quadratic Cost Function 110 5.8 Control Processes with Probabilistic Duration 113 5.8.1 An Optimal Economic Lot Size Problem 114 A. The Discrete Version and a Directed Computational A lgorithm 114 B. A Continuous Version and the Method of Successive Approximations 115 5.8.2 An Optimal Component Replacement Process 118 A. The Discrete Version and a Directed Computational Algorithm 118 B. A Continuous Version and the Method of Successive Approximations 121 5.9 Dynamic Programming and Investment Analysis 122 5.9.1 Dynamic Programming, Investment Values and the Present Worth Concept 122 5.9.2 The Use of Expected Yield in Stockmarket Investments 127 5.9.3 The Optimal Use of Reserve Cash 128 5.10 Dynamic Programming in Selling and Purchasing 130 5.10.1 The Optimal Disposal of an asset 130 5.10.2 Optimal Purchasing with Deadline 132 CHAPTER 6 ADAPTIVE PROCESSES 6.1 Describing the Problem Situation 6.2 Comparison of Dynamic Programming and the Statistical Decision Function Approach 6.3 Sufficient Statistics 6.4 Examples 6.4.1 Estimating a Parameter 6.4.2 Large Batch Sampling 6.4.3 An Adaptive Version of the Economic Lot Size Problem 6.4.4 A Pricing Problem 6.4.5 A Capacity Expansion Problem 6.4.6 A Search Problem 134 134 136 139 140 140 142 146 149 150 152 CONTRNTS APPENDICES PROOF OF SOME RESULTS Appendix to Chapter 1: The Classical Optimisation Problem Appendix to Chapter 2: The Optimal Path Problem Appendix to Chapter 3: The Nature of Dynamic Programming Appendix to Chapter 4: Deterministic Processes Appendix to Chapter 5: Stochastic Processes Appendix to Chapter 6: Adaptive Processes REFERENCES INDEX vii 155 157 160 163 165 169 171 179 181

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