Decision-dependent probabilities in stochastic programs with recourse

• Published in: Computational management science Vol. 15; no. 3-4; pp. 369 - 395
• Main Authors: Hellemo, Lars, Barton, Paul I., Tomasgard, Asgeir
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2018; Springer Nature B.V
• Subjects: Affine transformations; Business and Management; Mathematical models; Mathematical programming; Operations Research/Decision Theory; Optimization; Original Paper; Probability; Probability theory; Taxonomy; Uncertainty; Selective Branching; Endogenous Uncertainty; Test Instances; Decision Dependent Uncertainty; Stochastic Programming
• ISSN: 1619-697X; 1619-6988
• DOI: 10.1007/s10287-018-0330-0

Stochastic programming with recourse usually assumes uncertainty to be exogenous. Our work presents modelling and application of decision-dependent uncertainty in mathematical programming including a taxonomy of stochastic programming recourse models with decision-dependent uncertainty. The work includes several ways of incorporating direct or indirect manipulation of underlying probability distributions through decision variables in two-stage stochastic programming problems. Two-stage models are formulated where prior probabilities are distorted through an affine transformation or combined using a convex combination of several probability distributions. Additionally, we present models where the parameters of the probability distribution are first-stage decision variables. The probability distributions are either incorporated in the model using the exact expression or by using a rational approximation. Test instances for each formulation are solved with a commercial solver, BARON, using selective branching.