Design of Near Optimal Decision Rules in Multistage Adaptive Mixed-Integer Optimization

• 成果类型: Article
• 署名作者: Bertsimas, Dimitris; Georghiou, Angelos
• 署名单位: Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2015.1365
• 发表日期: 2015
• 页码: 610-627
• 关键词: uncertain linear-programs; robust optimization; inequalities; policies; systems; sums

摘要

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.