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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| Published in: | Computers & operations research Vol. 35; no. 6; pp. 2093 - 2102 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Oxford
Elsevier Ltd
01.06.2008
Elsevier Science Pergamon Press Inc |
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| ISSN: | 0305-0548, 1873-765X, 0305-0548 |
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| Abstract | 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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| AbstractList | 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. 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. [PUBLICATION ABSTRACT] |
| Author | Assavapokee, Tiravat Realff, Matthew J. Ammons, Jane C. Hong, I-Hsuan |
| Author_xml | – sequence: 1 givenname: Tiravat surname: Assavapokee fullname: Assavapokee, Tiravat email: Tiravat.Assavapokee@mail.uh.edu organization: Industrial Engineering, University of Houston, E206 Engineering Building 2, Houston, TX 77204-4008, USA – sequence: 2 givenname: Matthew J. surname: Realff fullname: Realff, Matthew J. email: Matthew.Realff@chbe.gatech.edu organization: Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0100, USA – sequence: 3 givenname: Jane C. surname: Ammons fullname: Ammons, Jane C. email: jane.ammons@isye.gatech.edu organization: Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA – sequence: 4 givenname: I-Hsuan surname: Hong fullname: Hong, I-Hsuan email: ihong@isye.gatech.edu organization: Georgia Institute of Technology, Atlanta, GA 30332-0205, USA |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Scenario relaxation algorithm for finite scenario-based min–max regret and min–max relative regret robust optimization |
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