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Mathematical Programming

, Volume 173, Issue 1–2, pp 393–430 | Cite as

Identifying effective scenarios in distributionally robust stochastic programs with total variation distance

  • Hamed Rahimian
  • Güzin BayraksanEmail author
  • Tito Homem-de-Mello
Full Length Paper Series A

Abstract

Traditional stochastic programs assume that the probability distribution of uncertainty is known. However, in practice, the probability distribution oftentimes is not known or cannot be accurately approximated. One way to address such distributional ambiguity is to work with distributionally robust convex stochastic programs (DRSPs), which minimize the worst-case expected cost with respect to a set of probability distributions. In this paper we analyze the case where there is a finite number of possible scenarios and study the question of how to identify the critical scenarios resulting from solving a DRSP. We illustrate that not all, but only some scenarios might have “effect” on the optimal value, and we formally define this notion for our general class of problems. In particular, we examine problems where the distributional ambiguity is modeled by the so-called total variation distance. We propose easy-to-check conditions to identify effective and ineffective scenarios for that class of problems. Computational results show that identifying effective scenarios provides useful insight on the underlying uncertainties of the problem.

Keywords

Stochastic programming Distributionally robust optimization Risk measures Scenario analysis 

Mathematics Subject Classification

90C15 90C47 

Notes

Acknowledgements

This work has been partially supported by the National Science Foundation through Grants CMMI-1345626 and CMMI-1563504 of the second author and CONICYT PIA Anillo ACT1407 (Chile) of the third author.

Supplementary material

10107_2017_1224_MOESM1_ESM.pdf (238 kb)
Supplementary material 1 (pdf 237 KB)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018

Authors and Affiliations

  1. 1.Department of Integrated Systems EngineeringThe Ohio State UniversityColumbusUSA
  2. 2.School of BusinessUniversidad Adolfo IbañezSantiagoChile

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