Design of Near Optimal Decision Rules in Multistage Adaptive Mixed-Integer Optimization
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Author(s)
Bertsimas, Dimitris J
Georghiou, Angelos
Date Issued
April 2015
Journal
Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Bertsimas, Dimitris and Angelos Georghiou. “Design of Near Optimal Decision Rules in Multistage Adaptive Mixed-Integer Optimization.” Operations Research 63, 3 (June 2015): 610–627 © 2015 INFORMS
Version
Original manuscript
Abstract
In recent years, decision rules have been established as the preferred solution method for addressing computationally demanding, multistage adaptive optimization problems. Despite their success, existing decision rules (a) are typically constrained by their a priori design and (b) do not incorporate in their modeling adaptive binary decisions. To address these problems, we first derive the structure for optimal decision rules involving continuous and binary variables as piecewise linear and piecewise constant functions, respectively. We then propose a methodology for the optimal design of such decision rules that have a finite number of pieces and solve the problem robustly using mixed-integer optimization. We demonstrate the effectiveness of the proposed methods in the context of two multistage inventory control problems. We provide global lower bounds and show that our approach is (i) practically tractable and (ii) provides high quality solutions that outperform alternative methods.
MIT Department
Massachusetts Institute of Technology. Process Systems Engineering Laboratory
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1287/OPRE.2015.1365
