Preprint
Distributionally Robust Optimization with Multimodal Decision-Dependent Ambiguity Sets
ArXiv.org
Cornell University
04/29/2024
DOI: 10.48550/arxiv.2404.19185
Abstract
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 $\phi$-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 $\phi$-divergence examples (variation distance and
$\chi^2$-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. We
provide a computational study over the facility location problem to illustrate
our results, which demonstrate that omission of multimodality and
decision-dependent uncertainties within DRO frameworks result in inadequately
performing solutions with worse in-sample and out-of-sample performances under
various settings.
Details
- Title: Subtitle
- Distributionally Robust Optimization with Multimodal Decision-Dependent Ambiguity Sets
- Creators
- Xian Yu - The Ohio State UniversityBeste Basciftci - University of Iowa
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2404.19185
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 04/29/2024
- Academic Unit
- Business Analytics
- Record Identifier
- 9984621182402771
Metrics
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