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

Hamed Rahimian, Güzin Bayraksan, Tito Homem-de-Mello

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

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.

Original languageEnglish
Pages (from-to)393-430
Number of pages38
JournalMathematical Programming
Volume173
Issue number1-2
DOIs
StatePublished - 23 Jan 2019
Externally publishedYes

Keywords

  • Distributionally robust optimization
  • Risk measures
  • Scenario analysis
  • Stochastic programming

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