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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 | |