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An Improved Three-Stage Algorithm with Bender’s Decomposition for Relative Robust Optimization under Full Factorial Scenario Design of Data Uncertainty

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Author(s): Wuthichai Wongthatsanekorn | Tiravat Assavapokee

Journal: International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies
ISSN 2228-9860

Volume: 2;
Issue: 1;
Start page: 111;
Date: 2011;
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Keywords: Relative Robust Optimization | Decision Making under Uncertainty | Min-Max Relative Regret | Full-Factorial Scenario Design | Benders’ Decomposition

ABSTRACT
This paper presents an improved decomposition algorithm for solving two-stage relative robust optimization problems under uncertainty. The structures of the first stage and second problem are a mixed integer linear programming model (MILP) and a linear programming model (LP) respectively. Each uncertain parameter in the model can independently take its value from a finite set of real values with unknown probability distribution. This structure of parametric uncertainty is called full-factorial scenario design of data. Similar to previous work, this improved algorithm composes of three stages. The difference is that Benders’ Decomposition (BD) algorithm is used to solve relaxed model in the first stage instead of the solver from CPLEX. The second and third stages are the same. The improved algorithm has been applied to solve a number of relative robust facility location problems under this structure of parametric uncertainty. All results illustrate significant improvement in computation time of the improved algorithm over existing approaches. For a problem with 3^40 possible scenarios, an improved algorithm shows a significant reduction in computational time by 61 percents comparing with the previous three-stage algorithm without Benders’ decomposition.
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