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Type Journal Article
Scope Discipline-based scholarship
Title A study of distributionally robust mixed-integer programming with Wasserstein metric: on the value of incomplete data
Organization Unit
Authors
  • Sergei Ketkov
Item Subtype Original Work
Refereed Yes
Status Published in final form
Language
  • English
Journal Title European Journal of Operational Research
Publisher Elsevier
Geographical Reach international
ISSN 0377-2217
Volume 313
Number 2
Page Range 602 - 615
Date 2024
Abstract Text This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in the underlying data set. The data uncertainty is described by a set of linear constraints for each random sample, and the uncertainty in the distribution (for a fixed realization of data) is defined using a type-1 Wasserstein ball centered at the empirical distribution of the data. The overall problem is formulated as a three-level distributionally robust optimization (DRO) problem. First, we prove that the three-level problem admits a single-level MILP reformulation, if the class of loss functions is restricted to biaffine functions. Secondly, it turns out that for several particular forms of data uncertainty, the outlined problem can be solved reasonably fast by leveraging the nominal MILP problem. Finally, we conduct a computational study, where the out-of-sample performance of our model and computational complexity of the proposed MILP reformulation are explored numerically for several application domains.
Digital Object Identifier 10.1016/j.ejor.2023.10.018
Other Identification Number merlin-id:24140
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