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List of Figures | |
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List of Tables | |
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Preface | |
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Notation | |
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Introduction | |
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Introduction | |
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Characteristics of Inventory Systems | |
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Brief Historical Overview of Inventory Theory | |
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Examples of Markovian Demand Models | |
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Contributions | |
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Plan of the Book | |
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Discounted Cost Models | |
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Discounted Cost Models with Backorders | |
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Introduction | |
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Review of the Related Literature | |
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Formulation of the Model | |
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Dynamic Programming and Optimal Feedback Policy | |
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Optimality of (s, S)-type Ordering Policies | |
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Nonstationary Infinite Horizon Problem | |
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Cyclic Demand Model | |
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Constrained Models | |
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Concluding Remarks and Notes | |
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Discounted Cost Models with Polynomially Growing Surplus Cost | |
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Introduction | |
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Formulation of the Model | |
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Dynamic Programming and Optimal Feedback Policy | |
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Nonstationary Discounted Infinite Horizon Problem | |
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Optimality of (s, S)-type Ordering Policies | |
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Stationary Infinite Horizon Problem | |
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Concluding Remarks and Notes | |
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Discounted Cost Models with Lost Sales | |
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Introduction | |
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Formulation of the Model | |
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Optimality of (s,S)-type Ordering Policies | |
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Extensions | |
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Numerical Results | |
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Concluding Remarks and Notes | |
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Average Cost Models | |
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Average Cost Models with Backorders | |
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Introduction | |
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Formulation of the Model | |
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Discounted Cost Model Results from Chapter 2 | |
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Limiting Behavior as the Discount Factor Approaches 1 | |
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Vanishing Discount Approach | |
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Verification Theorem | |
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Concluding Remarks and Notes | |
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Average Cost Models with Polynomially Growing Surplus Cost | |
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Formulation of the Problem | |
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Behavior of the Discounted Cost Model with Respect to the Discount Factor | |
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Vanishing Discount Approach | |
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Verification Theorem | |
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Concluding Remarks and Notes | |
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Average Cost Models with Lost Sales | |
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Introduction | |
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Formulation of the Model | |
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Discounted Cost Model Results from Chapter 4 | |
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Limiting Behavior as the Discount Factor Approaches 1 | |
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Vanishing Discount Approach | |
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Verification Theorem | |
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Concluding Remarks and Notes | |
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Miscellaneous | |
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Models With Demand Influenced By Promotion | |
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Introduction | |
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Formulation of the Model | |
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Assumptions and Preliminaries | |
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Structural Results | |
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Extensions | |
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Numerical Results | |
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Concluding Remarks and Notes | |
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Vanishing Discount Approach Vs. Stationary Distribution Approach | |
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Introduction | |
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Statement of the Problem | |
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Review of Iglehart (1963b) | |
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An Example | |
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Asymptotic Bounds on the Optimal Cost Function | |
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Review of the Veinott and Wagner Paper | |
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Existence of Minimizing Values of s and S | |
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Stationary Distribution Approach versus Dynamic Programming and Vanishing Discount Approach | |
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Concluding Remarks and Notes<p>206</p><l>1</l><l>Part V</l> | |
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Conclusions and Open Research Problems | |
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Appendices | |
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Analysis | |
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Continuous Functions on Metric Spaces | |
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Convergence of a Sequence of Functions | |
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The Arzela-Ascoli Theorems | |
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Linear Operators | |
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Miscellany | |
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Probability | |
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Integrability | |
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Conditional Expectation | |
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Renewal Theorem | |
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Renewal Reward Processes | |
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Stochastic Dominance | |
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Markov Chains | |
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Convex, Quasi-Convex and K-Convex Functions | |
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PF<sub>2</sub> Density and Quasi-convex Functions | |
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Convex and K-convex Functions | |
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References | |
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Copyright Permissions | |
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Author Index | |
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Subject Index | |