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| Preface | |
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| Conventions | |
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| Two Basic Models | |
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| The EOQ Model | |
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| The Newsvendor Model | |
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| Exercises | |
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| References | |
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| Recursion | |
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| Solving a Triangular System of Equations | |
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| Probabilistic Analysis of Models | |
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| Proof by Mathematical Induction | |
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| Shortest-Route Problems | |
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| Stochastic Shortest-Route Problems | |
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| Deterministic Production Planning | |
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| Knapsack Problems | |
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| Exercises | |
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| References | |
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| Finite-Horizon Markov Decision Processes | |
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| Example: e-Rite-Way | |
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| General Vocabulary and Basic Results | |
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| Exercises | |
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| References | |
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| Characterizing the Optimal Policy | |
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| Example: The Parking Problem | |
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| Dynamic Inventory Management | |
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| Preservation and Attainment | |
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| Exercises | |
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| References | |
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| Finite-Horizon Theory | |
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| Finite-State and -Action Theory | |
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| Proofs for the Finite-State and -Action Case | |
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| Generalizations | |
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| Optimality of Structured Policies | |
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| Exercises | |
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| References | |
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| Myopic Policies | |
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| General Approaches to Finding Solutions | |
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| Development | |
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| Application to Inventory Theory | |
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| Application to Reservoir Management | |
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| Extensions | |
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| Exercises | |
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| References | |
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| Dynamic Inventory Models | |
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| Optimality of (s, S) Inventory Policies | |
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| Linear-Quadratic Model | |
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| Exercises | |
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| References | |
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| Monotone Optimal Policies | |
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| Intuition | |
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| Lattices and Submodular Functions | |
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| A Dynamic Case | |
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| Capacitated Inventory Management | |
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| Exercises | |
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| References | |
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| Structured Probability Distributions | |
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| Some Interesting Distributions | |
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| Quasi-K-Convexity | |
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| A Variation of the (s, S) Inventory Model | |
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| Generalized (s, S) Policies | |
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| Exercises | |
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| References | |
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| Empirical Bayesian Inventory Models | |
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| Model Formulation | |
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| Conjugate Priors | |
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| Scalable Problems | |
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| Dimensionality Reduction | |
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| Exercises | |
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| References | |
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| Infinite-Horizon Theory | |
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| Problem Formulation | |
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| Mathematical Preparations | |
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| Finite State and Action Theory | |
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| Generalizations | |
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| Exercises | |
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| References | |
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| Bounds and Successive Approximations | |
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| Preliminary Results | |
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| Elimination of Nonoptimal Actions | |
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| Additional Topics | |
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| Exercises | |
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| References | |
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| Computational Markov Decision Processes | |
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| Policy Iteration | |
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| Use of Linear Programming | |
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| Preparations for Further Analysis | |
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| Convergence Rates for Value Iteration | |
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| Bounds on the Subradius | |
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| Transformations | |
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| Exercises | |
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| References | |
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| A Continuous Time Model | |
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| A Two-Product Production/Inventory Model | |
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| Formulation and Initial Analysis | |
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| Results | |
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| Exercises | |
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| References | |
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| Convexity | |
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| Basic Definitions and Results | |
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| Role of the Hessian | |
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| Generalizations of Convexity | |
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| Exercises | |
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| References | |
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| Duality | |
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| Basic Concepts | |
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| The Everett Result | |
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| Duality | |
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| Exercises | |
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| References | |
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| Discounted Average Value | |
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| Net Present Value | |
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| Discounted Average Value | |
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| Alternatives with Different Time Horizons | |
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| Approximating the DAV | |
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| Application to the EOQ Model | |
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| Random Cycle Lengths | |
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| Random-Yield EOQ Problem | |
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| Exercises | |
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| References | |
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| Preference Theory and Stochastic Dominance | |
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| Basic Concepts | |
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| Stochastic Dominance | |
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| How to Define Variability | |
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| Application to the Newsvendor Problem | |
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| Exercises | |
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| References | |
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| Index | |