Stochastic Modeling and Optimization With Applications in Queues, Finance, and Supply Chains

The objective of this volume is to highlight through a collection of chap­ ters some of the recent research works in applied prob ability, specifically stochastic 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 stochastic optimal control (Chapter 2); stochastic approximation, emphasizing convergence properties (Chapter 3); a performance-potential based approach to Markov decision program­ ming (Chapter 4); and interior-point techniques (homogeneous self-dual embedding and central path following) applied to stochastic programming (Chapter 5). The three chapters in the second part are concerned with queueing the­ ory. 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.

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 Stochastic 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 Stochastic Programming.- 5.1 Two-Stage Stochastic Linear Programming.- 5.2 A Case Study.- 5.3 Multiple Stage Stochastic 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 Stochastic Processing Networks.- 6.1 Preliminaries.- 6.2 Stochastic Processing Network Model.- 6.3 Examples of Stochastic Processing Networks.- 6.4 Brownian Model for Stochastic 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 Stochastic 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 Stochastic 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 Stochastic 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.

This book covers the brod range of research in stochastic models and optimization. Applications covered include networks, financial engineering, production planning and supply chain management. Each contribution is self-contained and written in an accessible style. this volume will be of interest to researchers and graduate students working in operations research, probability and statistics.