Distributionally robust optimization with multimodal decision-dependent ambiguity sets

• 成果类型: Article; Early Access
• 署名作者: Yu, Xian; Basciftci, Beste
• 署名单位: University System of Ohio; Ohio State University; University of Iowa
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-026-02337-1
• 发表日期: 2026-03-09
• 关键词: distributionally robust optimization; Multimodal uncertainty; decision-dependent uncertainty; Moment-based ambiguity set; Wasserstein distance-based ambiguity set; 90; linear-programs; reformulations; algorithm

摘要

We consider a two-stage distributionally robust optimization (DRO) model with multimodal uncertainty, where both the mode probabilities and uncertainty distributions could be affected by the first-stage decisions. To address this setting, we propose a generic framework by introducing a phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document}-divergence based ambiguity set to characterize the decision-dependent mode probabilities and further consider both moment-based and Wasserstein distance-based ambiguity sets to characterize the uncertainty distribution under each mode. We identify two special phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document}-divergence examples (variation distance and chi 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi <^>2$$\end{document}-distance) and provide specific forms of decision dependence relationships under which we can derive tractable reformulations. Furthermore, we investigate the benefits of considering multimodality in a DRO model compared to a single-modal counterpart through an analytical analysis. Additionally, we develop a separation-based decomposition algorithm to solve the resulting multimodal decision-dependent DRO models with finite convergence and optimality guarantee under certain settings. We provide a detailed computational study over two example problem settings, the facility location problem and shipment planning problem with pricing, to illustrate our results, which demonstrate that omission of multimodality or decision-dependent uncertainties within DRO frameworks result in inadequately performing solutions with worse in-sample and out-of-sample performances under various settings. We further demonstrate the speed-ups obtained by the solution algorithm against the off-the-shelf solver over various instances.