Exploiting the Structure of Two-Stage Robust Optimization Models with Exponential Scenarios
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ijc19.pdf
Description
Accepted version
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797.52 KB
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Adobe PDF
Checksum (MD5)
9f48da3b186d08e83fca40b0d798a23b
Author(s)
Jaillet, Patrick
Date Issued
June 2020
Journal
INFORMS Journal on Computing
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Doulabi, Hossein Hashemi et al. “Exploiting the Structure of Two-Stage Robust Optimization Models with Exponential Scenarios.” INFORMS Journal on Computing (June 2020) © 2020 The Author(s)
Version
Author's final manuscript
Abstract
This paper addresses a class of two-stage robust optimization models with an exponential number of scenarios given implicitly. We apply Dantzig–Wolfe decomposition to exploit the structure of these models and show that the original problem reduces to a single-stage robust problem. We propose a Benders algorithm for the reformulated single-stage problem. We also develop a heuristic algorithm that dualizes the linear programming relaxation of the inner maximization problem in the reformulated model and iteratively generates cuts to shape the convex hull of the uncertainty set. We combine this heuristic with the Benders algorithm to create a more effective hybrid Benders algorithm. Because the master problem and subproblem in the Benders algorithm are mixed-integer programs, it is computationally demanding to solve them optimally at each iteration of the algorithm. Therefore, we develop novel stopping conditions for these mixed-integer programs and provide the relevant convergence proofs. Extensive computational experiments on a nurse planning problem and a two-echelon supply chain problem are performed to evaluate the efficiency of the proposed algorithms.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/IJOC.2019.0928
