Scenario relaxation algorithm for finite scenario-based min–max regret and min–max relative regret robust optimization

Most practical decision-making problems are compounded in difficulty by the degree of uncertainty and ambiguity surrounding the key model parameters. Decision makers may be confronted with problems in which no sufficient historical information is available to make estimates of the probability distri...

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Bibliographic Details
Published in:Computers & operations research Vol. 35; no. 6; pp. 2093 - 2102
Main Authors: Assavapokee, Tiravat, Realff, Matthew J., Ammons, Jane C., Hong, I-Hsuan
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 01.06.2008
Elsevier Science
Pergamon Press Inc
Subjects:
Algorithms
Applied sciences
Computer science; control theory; systems
Data processing. List processing. Character string processing
Decision making
Decision making models
Decision theory. Utility theory
Exact sciences and technology
Integer programming
Linear programming
Mathematical programming
Memory organisation. Data processing
Min–max regret
Min–max relative regret
Operational research and scientific management
Operational research. Management science
Optimization algorithms
Parameter estimation
Robust optimization
Scenario-based decision-making
Scenarios
Software
Studies
Uncertainty
Scenarios
Robust optimization
Min–max regret
Scenario-based decision-making
Min–max relative regret
Termination problem
Psychology
Iterative method
Probability distribution
Modeling
Linear model
Optimization
Min-max regret
Uncertain system
Min-max relative regret
Mathematical programming
Script
Decision support system
Decision making
Linear programming
Mixed integer programming
Long term
Mixed model
Optimal solution
Minimax method
Mixed problem
Ambiguity
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary:Most practical decision-making problems are compounded in difficulty by the degree of uncertainty and ambiguity surrounding the key model parameters. Decision makers may be confronted with problems in which no sufficient historical information is available to make estimates of the probability distributions for uncertain parameter values. In these situations, decision makers are not able to search for the long-term decision setting with the best long-run average performance. Instead, decision makers are searching for the robust long-term decision setting that performs relatively well across all possible realizations of uncertainty without attempting to assign an assumed probability distribution to any ambiguous parameter. In this paper, we propose an iterative algorithm for solving min–max regret and min–max relative regret robust optimization problems for two-stage decision-making under uncertainty (ambiguity) where the structure of the first-stage problem is a mixed integer (binary) linear programming model and the structure of the second-stage problem is a linear programming model. The algorithm guarantees termination at an optimal robust solution, if one exists. A number of applications of the proposed algorithm are demonstrated. All results illustrate good performance of the proposed algorithm.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2006.10.013