The art and theory of dynamic programming, Volume 130 (Mathematics in Science and Engineering)

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 Approach
	5. 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 Formulation
	3. 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 Problem
	5. 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 Problem
Chapter 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
	3. Computational Procedures
	References
Chapter 14. Stochastic Problems with Linear Dynamics and Quadratic Criteria
	1. Introduction
	2. Certainty Equivalence
	3. A More General Stochastic Model
Chapter 15. Optimization Problems Involving Learning
	1. Introduction
	2. Bayes’ Law
	3. A Shortest-Path Problem with Learning
	4. A Quality Control Problem
	5. Decision Analysis
	6. A Linear Dynamics, Quadratic Criterion Problem with Learning
Problem Solutions
Index