A Linear Decision-Based Approximation Approach to Stochastic Programming

Stochastic optimization, especially multistage models, is well known to be computationally excruciating. Moreover, such models require exact specifications of the probability distributions of the underlying uncertainties, which are often unavailable. In this paper, we propose tractable methods of ad...

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Veröffentlicht in:Operations research Jg. 56; H. 2; S. 344 - 357
Hauptverfasser: Chen, Xin, Sim, Melvyn, Sun, Peng, Zhang, Jiawei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Linthicum, MD INFORMS 01.03.2008
Institute for Operations Research and the Management Sciences
Schlagworte:
Analysis
Applied sciences
Approximation
Covariance
Decision making
Decision theory. Utility theory
Exact sciences and technology
Linear programming
Mathematical vectors
Mathematics
Matrices
Objective functions
Operational research and scientific management
Operational research. Management science
Optimization
programming
Random variables
Robust optimization
Sampling methods
stochastic
Stochastic models
Stochastic programming
Studies
United States
Stochastic model
conic programming
Probabilistic approach
programming: stochastic
Stochastic approximation
Modeling
Stochastic programming
Decision rule
Uncertain system
Covariance
Limit distribution
Linear approximation
Model specification
ISSN:0030-364X, 1526-5463
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:Stochastic optimization, especially multistage models, is well known to be computationally excruciating. Moreover, such models require exact specifications of the probability distributions of the underlying uncertainties, which are often unavailable. In this paper, we propose tractable methods of addressing a general class of multistage stochastic optimization problems, which assume only limited information of the distributions of the underlying uncertainties, such as known mean, support, and covariance. One basic idea of our methods is to approximate the recourse decisions via decision rules. We first examine linear decision rules in detail and show that even for problems with complete recourse, linear decision rules can be inadequate and even lead to infeasible instances. Hence, we propose several new decision rules that improve upon linear decision rules, while keeping the approximate models computationally tractable. Specifically, our approximate models are in the forms of the so-called second-order cone (SOC) programs, which could be solved efficiently both in theory and in practice. We also present computational evidence indicating that our approach is a viable alternative, and possibly advantageous, to existing stochastic optimization solution techniques in solving a two-stage stochastic optimization problem with complete recourse.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1070.0457