Stochastic Modeling and Optimization: With Applications in Queues, Finance, and Supply Chains / Edition 1

by David D. Yao, Hanqin Zhang, Xun Yu Zhou

Overview

The objective of this volume is to highlight through a collection of chapters some of the recent research works in applied prob ability, specifically shastic modeling and optimization. The volume is organized loosely into four parts. The first part is a col­ lection of several basic methodologies: singularly perturbed Markov chains (Chapter 1), and related applications in shastic optimal control (Chapter 2); shastic approximation, emphasizing convergence properties (Chapter 3); a performance-potential based approach to Markov decision programming (Chapter 4); and interior-point techniques (homogeneous self-dual embedding and central path following) applied to shastic programming (Chapter 5). The three chapters in the second part are concerned with queueing theory. Chapters 6 and 7 both study processing networks - a general dass of queueing networks - focusing, respectively, on limit theorems in the form of strong approximation, and the issue of stability via connections to re­ lated fluid models. The subject of Chapter 8 is performance asymptotics via large deviations theory, when the input process to a queueing system exhibits long-range dependence, modeled as fractional Brownian motion.

Product Details

ISBN-13:	9780387955827
Publisher:	Springer New York
Publication date:	01/14/2003
Series:	Springer Series in Operations Research
Edition description:	2003
Pages:	468
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1 Discrete-time Singularly Perturbed Markov Chains.- 1.1 Singularly Perturbed Markov Chains.- 1.2 Asymptotic Expansions.- 1.3 Occupation Measures.- 1.4 Nonstationary Markov Chains and Applications.- 1.5 Notes and Remarks.- 1.6 References.- 2 Nearly Optimal Controls of Markovian Systems.- 2.1 Singularly Perturbed MDP.- 2.2 Hybrid LQG Control.- 2.3 Conclusions.- 2.4 References.- 3 Shastic Approximation, with Applications.- 3.1 SA Algorithms.- 3.2 General Convergence Theorems by TS Method.- 3.3 Convergence Theorems Under State-Independent Conditions.- 3.4 Applications.- 3.5 Notes.- 3.6 References.- 4 Performance Potential Based Optimization and MDPs.- 4.1 Sensitivity Analysis and Performance Potentials.- 4.2 Markov Decision Processes.- 4.3 Problems with Discounted Performance Criteria.- 4.4 Single Sample Path Based Implementations.- 4.5 Time Aggregation.- 4.6 Connections to Perturbation Analysis.- 4.7 Application Examples.- 4.8 Notes.- 4.9 References.- 5 An Interior-Point Approach to Multi-Stage Shastic Programming.- 5.1 Two-Stage Shastic Linear Programming.- 5.2 A Case Study.- 5.3 Multiple Stage Shastic Programming.- 5.4 An Interior Point Method.- 5.5 Finding Search Directions.- 5.6 Model Diagnosis.- 5.7 Notes.- 5.8 References.- 6 A Brownian Model of Shastic Processing Networks.- 6.1 Preliminaries.- 6.2 Shastic Processing Network Model.- 6.3 Examples of Shastic Processing Networks.- 6.4 Brownian Model for Shastic Processing Network.- 6.5 Brownian Approximation via Strong Approximation.- 6.6 Notes.- 6.7 Appendix: Strong Approximation vs. Heavy Traffic Approximation.- 6.8 References.- 7 Stability of General Processing Networks.- 7.1 Motivating Simulations.- 7.2 Open Processing Networks.- 7.3 Network and Fluid Model Equations.- 7.4 Connection betweenArtificial and Standard Fluid Models.- 7.5 Examples of Stable Policies.- 7.6 Extensions.- 7.7 Appendix.- 7.8 Notes.- 7.9 References.- 8 Large Deviations, Long-Range Dependence, and Queues.- 8.1 Fractional Brownian Motion and a Related Filter.- 8.2 Moderate Deviations for Sample-Path Processes.- 8.3 MDP for the Filtered Process.- 8.4 Queueing Applications: The Workload Process.- 8.5 Verifying the Key Assumptions.- 8.6 Notes.- 8.7 References.- 9 Markowitz’s World in Continuous Time, and Beyond.- 9.1 The Mean-Variance Portfolio Selection Model.- 9.2 A Shastic LQ Control Approach.- 9.3 Efficient Frontier: Deterministic Market Parameters.- 9.4 Efficient Frontier: Random Adaptive Market Parameters.- 9.5 Efficient Frontier: Markov-Modulated Market Parameters.- 9.6 Efficient Frontier: No Short Selling.- 9.7 Mean-Variance Hedging.- 9.8 Notes.- 9.9 References.- 10 Variance Minimization in Shastic Systems.- 10.1 Variance Minimization Problem.- 10.2 General Variance Minimization Problem.- 10.3 Variance Minimization in Dynamic Portfolio Selection.- 10.4 Variance Minimization in Dual Control.- 10.5 Notes.- 10.6 References.- 11 A Markov Chain Method for Pricing Contingent Claims.- 11.1 The Markov Chain Pricing Method.- 11.2 The Black-Scholes (1973) Pricing Model.- 11.3 The GARCH Pricing Model.- 11.4 Valuing Exotic Options.- 11.5 Appendix: The Conditional Expected Value of hT* and hT*2.- 11.6 References.- 12 Shastic Network Models and Optimization of a Hospital System.- 12.1 A Multi-Site Service Network Model.- 12.2 Patient Flow Management.- 12.3 Capacity Design.- 12.4 Switching Costs and Quality of Service.- 12.5 Insights and Future Research Directions.- 12.6 Notes.- 12.7 References.- 13 Optimal Airline Booking Control with Cancellations.- 13.1 Preliminaries.- 13.2 TheMinimum Acceptable Fare and Threshold Control.- 13.3 Extensions of the Basic Model.- 13.4 Numerical Experiments.- 13.5 Notes.- 13.6 References.- 14 Information Revision and Decision Making in Supply Chain Management.- 14.1 Industrial Examples.- 14.2 A Multi-Period, Two-Decision Model.- 14.3 A One-Period, Multi-Information Revision Model.- 14.4 Applications.- 14.5 Notes.- 14.6 References.- About the Contributors.

Editorial Reviews

From the reviews:

"The Workshop Shastic Models and Optimization … in May 2001, forms the basis of the present volume. 14 papers from about 60 presentations at the workshop were selected and thoroughly revised making self-contained chapters of a book for a broad audience. It highlighted some recent advances in applied probability achieved mainly by scientists with Chinese background. … The book seems to be very suitable for seminar studies at the graduate level." (Hans-Joachim Girlich, OR News, 25, November 2005)

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