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1448. Solving Two-Stage Stochastic Programs with Endogenous Uncertainty via Random Variable Transformation

Invited abstract in session TC-35: Stochastic Optimization with Decision-Dependent Uncertainty, stream Stochastic, Robust and Distributionally Robust Optimization.

Tuesday, 12:30-14:00
Room: 44 (building: 303A)

Authors (first author is the speaker)

1. Maria Carolina Bazotte Corgozinho
Mathematics and Industrial Engineering Department, Polytechnique Montreal
2. Margarida Carvalho
Université de Montréal
3. Thibaut Vidal
Mathematics and Industrial Engineering, Polytechnique Montréal

Abstract

Real-world decision-making problems involve decision-dependent uncertainty, where the probability distribution of the random vector depends on the model decisions. However, few studies focus on two-stage stochastic programs with this type of endogenous uncertainty, and those that do lack general methodologies. We thus propose a general method for solving a class of these programs based on random variable transformation, a technique widely employed in probability and statistics. The random variable transformation converts a stochastic program with endogenous uncertainty (original program) into an equivalent stochastic program with decision-independent uncertainty (transformed program), for which solution procedures are well-studied. Moreover, endogenous uncertainty usually leads to nonlinear nonconvex programs, which are theoretically intractable. Nonetheless, we show that, for some classical endogenous distributions, the proposed method yields mixed-integer linear or convex programs with exogenous uncertainty. We validate this method by applying it to a network design and facility-protection problem, considering distinct decision-dependent distributions for the random variables. Whereas the original formulation of this problem is nonlinear nonconvex for most endogenous distributions, the proposed method transforms it into mixed-integer linear programs with exogenous uncertainty. We solve these obtained programs with the sample average approximation (SAA) method.

Keywords

Status: accepted

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