Optimization of Stochastic Models: The Interface Between Simulation and Optimization / Edition 1

by Georg Ch. Pflug

Overview

Shastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are shastic in nature. Shastic models are considered in transportation and communication. Marketing models use shastic descriptions of the demands and buyer's behaviors. In finance, market prices and exchange rates are assumed to be certain shastic processes, and insurance claims appear at random times with random amounts.
To each decision problem, a cost function is associated. Costs may be direct or indirect, like loss of time, quality deterioration, loss in production or dissatisfaction of customers. In decision making under uncertainty, the goal is to minimize the expected costs. However, in practically all realistic models, the calculation of the expected costs is impossible due to the model complexity. Simulation is the only practicable way of getting insight into such models. Thus, the problem of optimal decisions can be seen as getting simulation and optimization effectively combined.
The field is quite new and yet the number of publications is enormous. This book does not even try to touch all work done in this area. Instead, many concepts are presented and treated with mathematical rigor and necessary conditions for the correctness of various approaches are stated.
Optimization of Shastic Models: The Interface Between Simulation and Optimization is suitable as a text for a graduate level course on Shastic Models or as a secondary text for a graduate level course in Operations Research.

Product Details

ISBN-13:	9780792397809
Publisher:	Springer US
Publication date:	09/30/1996
Series:	The Springer International Series in Engineering and Computer Science , #373
Edition description:	1996
Pages:	382
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1 Optimization.- 1.1 Shastic optimization problems.- 1.2 Approximations.- 1.3 Bounds.- 1.4 Deterministic optimization procedures and their shastic counterparts.- 1.5 Discrete Optimization.- 2 Discrete-Event processes.- 2.1 Markov chains with discrete time.- 2.2 Markov chains with continuous time.- 2.3 MARKOV PROCESSES WITH ARBITRARY STATE SPACE.- 2.4 Semi-Markov processes.- 2.5 Generalized Semi-Markov processes.- 2.6 Queueing processes.- 3 Derivatives.- 3.1 Derivatives of random processes.- 3.2 Derivatives of probability measures.- 3.3 Derivative concepts for Markov processes.- 4 Simulation and sensitivity estimation.- 4.1 Simulation techniques.- 4.2 Simulation of derivatives for random variables.- 4.3 Simulation of sensitivities for Markov Processes.- 4.4 Estimation of derivatives of Discrete-Event processes.- 5 Shastic Approximation.- 5.1 Convergence and asymptotic distributions.- 5.2 Stopping times and confidence regions.- 5.3 DISCRETE STOCHASTIC APPROXIMATION.- 5.4 Shastic Approximation versus the Response Surface Method.- 5.5 The convergence of the combined procedure.- A Metric spaces.- B Sequences and Series.- C Matrix Algebra.- D Derivatives.- E Convexity and convex projections.- F Set-wise Convergence.- G Duality and Lagrangians.- H Probability spaces and random variables.- I Convergence of random variables.- J The Wasserstein distance.- K Conditional expectations.- L Martingales.- M Choquet Theory.- N Coupling.

Editorial Reviews

Intended for graduate courses on Stochastic Models or Operations Research, this text does not even try to touch all the work done in this new field. Instead, many concepts are presented and treated with mathematical rigor, and necessary conditions for the correctness of various approaches are stated. Topics include stochastic optimization, approximations, and bounds; discrete-event processes, including Markov chains and queueing processes; derivatives of random processes and of probability measures; and simulation and sensitivity estimation. Annotation c. by Book News, Inc., Portland, Or.

Booknews