Foundations of Stochastic Inventory Theory

ISBN-10: 0804743991
ISBN-13: 9780804743990
Edition: 2002
Authors: Evan L. Porteus
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Book details

List price: $57.50
Copyright year: 2002
Publisher: Stanford University Press
Publication date: 8/9/2002
Binding: Hardcover
Pages: 320
Size: 6.38" wide x 9.25" long x 0.90" tall
Weight: 1.408

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

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