The art and theory of dynamic programming / Stuart E. Dreyfus, Averill M. Law.

Includes bibliographical references and index.

Print version record.

Front Cover; The Art and Theory of Dynamic Programming; Copyright Page; Contents; Preface; Acknowledgments; Chapter 1. Elementary Path Problems; 1. Introduction; 2. A Simple Path Problem; 3. The Dynamic-Programming Solution; 4. Terminology; 5. Computational Efficiency; 6. Forward Dynamic Programming; 7. A More Complicated Example; 8. Solution of the Example; 9. The Consultant Question; 10. Stage and State; 11. The Doubling-Up Procedure; Chapter 2. Equipment Replacement; 1. The Simplest Model; 2. Dynamic-Programming Formulation; 3. Shortest-Path Representation of the Problem

4. Regeneration Point Approach5. More Complex Equipment-Replacement Models; Chapter 3. Resource Allocation; 1. The Simplest Model; 2. Dynamic-Programming Formulation; 3. Numerical Solution; 4. Miscellaneous Remarks; 5. Unspecified Initial Resources; 6. Lagrange Multipliers; 7. Justification of the Procedure; 8. Geometric Interpretation of the Procedure; 9. Some Additional Cases; 10. More Than Two Constraints; Chapter 4. The General Shortest-Path Problem; 1. Introduction; 2. Acyclic Networks; 3. General Networks; References; Chapter 5. The Traveling-Salesman Problem; 1. Introduction

2. Dynamic-Programming Formulation3. A Doubling-Up Procedure for the Case of Symmetric Distances; 4. Other Versions of the Traveling-Salesman Problem; Chapter 6. Problems with Linear Dynamics and Quadratic Criteria; 1. Introduction; 2. A Linear Dynamics, Quadratic Criterion Model; 3. A Particular Problem; 4. Dynamic-Programming Solution; 5. Specified Terminal Conditions; 6. A More General Optimal Value Function; Chapter 7. Discrete-Time Optimal-Control Problems; 1. Introduction; 2. A Necessary Condition for the Simplest Problem; 3. Discussion of the Necessary Condition

4. The Multidimensional Problem5. The Gradient Method of Numerical Solution; Chapter 8. The Cargo-Loading Problem; 1. Introduction; 2. Algorithm 1; 3. Algorithm 2; 4. Algorithm 3; 5. Algorithm 4; References; Chapter 9. Stochastic Path Problems; 1. Introduction; 2. A Simple Problem; 3. What Constitutes a Solution?; 4. Numerical Solutions of Our Example; 5. A Third Control Philosophy; 6. A Stochastic Stopping-Time Problem; 7. Problems with Time-Lag or Delay; Chapter 10. Stochastic Equipment Inspection and Replacement Models; 1. Introduction; 2. Stochastic Equipment-Replacement Models

3. An Inspection and Replacement ProblemChapter 11. Dynamic Inventory Systems; 1. The Nature of Inventory Systems; 2. Models with Zero Delivery Lag; 3. Models with Positive Delivery Lag; 4. A Model with Uncertain Delivery Lag; Chapter 12. Inventory Models with Special Cost Assumptions; 1. Introduction; 2. Convex and Concave Cost Functions; 3. Models with Deterministic Demand and Concave Costs; 4. Optimality of (s, S ) Policies; 5. Optimality of Single Critical Number Policies; References; Chapter 13. Markovian Decision Processes; 1. Introduction; 2. Existence of an Optimal Policy

The art and theory of dynamic programming.

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