Stochastic Modeling and Optimization

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

• ISBN13: 9780387955827
• ISBN10: 0387955828
• Format: Hardcover
• Copyright: 2003-02-01
• Publisher: Springer Verlag

Summary

This book covers the broad range of research in stochastic models and optimization. Applications covered include networks, financial engineering, production planning and supply chain management. Each contribution is aimed at graduate students working in operations research, probability, and statistics.

Table of Contents

Preface	v
Discrete-time Singularly Perturbed Markov Chains	1	(42)
G. Yin
Q. Zhang
Singularly Perturbed Markov Chains	2	(10)
Motivation	2	(1)
Preliminary	3	(2)
Singularly Perturbed Models	5	(4)
Motivating Examples	9	(3)
Asymptotic Expansions	12	(6)
Occupation Measures	18	(5)
Nonstationary Markov Chains and Applications	23	(13)
Asymptotic Properties for Smooth Transition Matrices	23	(6)
Bounded and Measurable Transition Matrices	29	(3)
Applications to Nearly Optimal Controls	32	(4)
Notes and Remarks	36	(2)
Notes on the Literature	36	(1)
Possible Future Research Topics	37	(1)
References	38	(5)
Nearly Optimal Controls of Markovian Systems	43	(44)
Q. Zhang
R.H. Liu
G. Yin
Singularly Perturbed MDP	44	(18)
Irreducible MDP under Discounted Cost	46	(5)
Irreducible MDP under Long-Run Average Cost	51	(3)
MDP with General Transition Matrices	54	(7)
Historical Notes	61	(1)
Hybrid LQG Control	62	(21)
Aggregation and Approximation	66	(5)
Asymptotic Optimality	71	(4)
Hybrid LQG with General Transition Matrices	75	(5)
A Numerical Example	80	(2)
Historical Notes	82	(1)
Conclusions	83	(1)
References	83	(4)
Stochastic Approximation, with Applications	87	(24)
Han-Fu Chen
SA Algorithms	87	(3)
General Convergence Theorems by TS Method	90	(9)
Convergence Theorems Under State-Independent Conditions	99	(3)
Applications	102	(5)
Application to Optimization	102	(3)
Application to Signal Processing	105	(2)
Notes	107	(1)
References	108	(3)
Performance Potential Based Optimization and MDPs	111	(26)
Xi-Ren Cao
Sensitivity Analysis and Performance Potentials	112	(4)
Markov Decision Processes	116	(2)
Problems with Discounted Performance Criteria	118	(3)
Single Sample Path Based Implementations	121	(2)
Time Aggregation	123	(3)
Connections to Perturbation Analysis	126	(2)
Application Examples	128	(2)
Notes	130	(4)
References	134	(3)
An Interior-Point Approach to Multi-Stage Stochastic Programming	137	(34)
Shuzhong Zhang
Two-Stage Stochastic Linear Programming	139	(3)
A Case Study	142	(2)
Multiple Stage Stochastic Programming	144	(2)
An Interior Point Method	146	(10)
Finding Search Directions	156	(8)
Model Diagnosis	164	(3)
Notes	167	(1)
References	168	(3)
A Brownian Model of Stochastic Processing Networks	171	(22)
Hong Chen
Preliminaries	172	(2)
Stochastic Processing Network Model	174	(2)
Examples of Stochastic Processing Networks	176	(5)
Scheduling Control of Multiclass Queueing Network	176	(1)
A Simple Queueing Network with both Scheduling and Routing	177	(2)
An Assemble-To-Order System	179	(2)
Brownian Model for Stochastic Processing Network	181	(4)
Comparison to Harrison's Brownian Model	183	(1)
Extensions	184	(1)
Brownian Approximation via Strong Approximation	185	(1)
Notes	186	(1)
Appendix: Strong Approximation vs. Heavy Traffic Approximation	187	(4)
References	191	(2)
Stability of General Processing Networks	193	(52)
Jim Dai
Otis B. Jennings
Motivating Simulations	195	(6)
Open Processing Networks	201	(9)
Network Description	202	(3)
The Standard Network and Dispatch Policies	205	(1)
Production Policies and Sensible Policies	206	(3)
Rate Stability	209	(1)
Network and Fluid Model Equations	210	(9)
Network Dynamics	210	(4)
Fluid Models	214	(3)
Connection between Processing Networks and Fluid Models	217	(2)
Connection between Artificial and Standard Fluid Models	219	(4)
Batch Processing Networks and Normal Policies	219	(3)
Stability under Sensible Production Policies	222	(1)
Examples of Stable Policies	223	(7)
Early Steps First	223	(5)
Generalized Round Robin	228	(2)
Extensions	230	(2)
Appendix	232	(8)
Departures As a Function of Server Effort	232	(4)
Proofs of Lemmas 7.12 and 7.18	236	(4)
Notes	240	(1)
References	241	(4)
Large Deviations, Long-Range Dependence, and Queues	245	(34)
C.-S. Chang
David D. Yao
Tim Zajic
Fractional Brownian Motion and a Related Filter	246	(2)
Moderate Deviations for Sample-Path Processes	248	(4)
MDP for the Filtered Process	252	(6)
Queueing Applications: The Workload Process	258	(9)
Verifying the Key Assumptions	267	(7)
Notes	274	(1)
References	275	(4)
Markowitz's World in Continuous Time, and Beyond	279	(32)
Xun Yu Zhou
The Mean--Variance Portfolio Selection Model	280	(3)
A Stochastic LQ Control Approach	283	(2)
Efficient Frontier: Deterministic Market Parameters	285	(7)
Efficient Frontier: Random Adaptive Market Parameters	292	(4)
Efficient Frontier: Markov-Modulated Market Parameters	296	(3)
Efficient Frontier: No Short Selling	299	(1)
Mean--Variance Hedging	300	(3)
Notes	303	(2)
References	305	(6)
Variance Minimization in Stochastic Systems	311	(22)
Duan Li
Fucai Qian
Peilin Fu
Variance Minimization Problem	311	(3)
General Variance Minimization Problem	314	(2)
Variance Minimization in Dynamic Portfolio Selection	316	(7)
Variance Minimization in Dual Control	323	(7)
Notes	330	(1)
References	330	(3)
A Markov Chain Method for Pricing Contingent Claims	333	(30)
Jin-Chuan Duan
Genevieve Gauthier
Jean-Guy Simonato
The Markov Chain Pricing Method	334	(2)
The Black-Scholes (1973) Pricing Model	336	(11)
Choosing the Set of Asset Prices	337	(1)
Computing Transition Probabilities and Option Prices	338	(1)
An Illustrative Example	339	(2)
A Markov Chain Interpretation of Binomial Tree	341	(2)
Numerical Examples	343	(4)
The GARCH Pricing Model	347	(8)
Choosing the Set of Discrete Prices and Volatilities	349	(1)
Computing Transition Probabilities and Option Prices	350	(1)
Numerical Examples	351	(4)
Valuing Exotic Options	355	(5)
Appendix: The Conditional Expected Value of hT* and h2T*	360	(1)
References	361	(2)
Stochastic Network Models and Optimization of a Hospital System	363	(32)
Xiuli Chao
Liming Liu
Shaohui Zheng
A Multi-Site Service Network Model	364	(2)
Patient Flow Management	366	(5)
Capacity Design	371	(11)
Switching Costs and Quality of Service	382	(5)
Insights and Future Research Directions	387	(3)
Notes	390	(1)
References	391	(4)
Optimal Airline Booking Control with Cancellations	395	(34)
Youyi Feng
Ping Lin
Baichun Xiao
Preliminaries	396	(4)
Model Description	396	(2)
Optimality Conditions and the Value Function	398	(2)
The Minimum Acceptable Fare and Threshold Control	400	(14)
The Minimum Acceptable Fare	400	(2)
Properties of MAF	402	(10)
Threshold Control and Computation of the Value Function	412	(2)
Extensions of the Basic Model	414	(4)
Time-Dependent Air Fares	414	(1)
Fare-Dependent Partial Refunds	414	(4)
Numerical Experiments	418	(3)
Notes	421	(3)
References	424	(5)
Information Revision and Decision Making in Supply Chain Management	429	(30)
Houmin Yan
Hanqin Zhang
Industrial Examples	429	(6)
The Procurement of Micro-Controller	430	(1)
Analysis of Demand Forecast Data	431	(4)
The Deregulated Energy Markets	435	(1)
A Multi-Period, Two-Decision Model	435	(8)
A One-Period, Multi-Information Revision Model	443	(7)
Applications	450	(1)
Decision-Making with Two Procurement Alternatives	450	(1)
The Application to Deregulated Energy Markets	450	(1)
Notes	451	(4)
References	455	(4)
About the Contributors	459