Technical Note—Two-Stage Sample Robust Optimization

Dimitris Bertsimas (), Shimrit Shtern () and Bradley Sturt ()
Additional contact information
Dimitris Bertsimas: Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Shimrit Shtern: The William Davidson Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Haifa 3200003, Israel
Bradley Sturt: Department of Information and Decision Sciences, University of Illinois at Chicago, Chicago, Illinois 60607

Operations Research, 2022, vol. 70, issue 1, 624-640

Abstract: We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type- ∞ Wasserstein ambiguity set. Our main result establishes that this approximation scheme is asymptotically optimal for two-stage stochastic linear optimization problems; that is, under mild assumptions, the optimal cost and optimal first-stage decisions obtained by approximating the robust optimization problem converge to those of the underlying stochastic problem as the number of data points grows to infinity. These guarantees notably apply to two-stage stochastic problems that do not have relatively complete recourse , which arise frequently in applications. In this context, we show through numerical experiments that the approximation scheme is practically tractable and produces decisions that significantly outperform those obtained from state-of-the-art data-driven alternatives.

Keywords: Optimization; stochastic programming; distributionally robust optimization; sample average approximation (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/opre.2020.2096 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:70:y:2022:i:1:p:624-640

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().