TY - JOUR

T1 - Identifying effective scenarios in distributionally robust stochastic programs with total variation distance

AU - Rahimian, Hamed

AU - Bayraksan, Güzin

AU - Homem-de-Mello, Tito

N1 - Funding Information:
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.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.

PY - 2019/1/23

Y1 - 2019/1/23

N2 - 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.

AB - 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.

KW - Distributionally robust optimization

KW - Risk measures

KW - Scenario analysis

KW - Stochastic programming

UR - http://www.scopus.com/inward/record.url?scp=85040792832&partnerID=8YFLogxK

U2 - 10.1007/s10107-017-1224-6

DO - 10.1007/s10107-017-1224-6

M3 - Article

AN - SCOPUS:85040792832

SN - 0025-5610

VL - 173

SP - 393

EP - 430

JO - Mathematical Programming

JF - Mathematical Programming

IS - 1-2

ER -