Decision-dependent probabilities in stochastic programs with recourse
Author(s)Hellemo, Lars; Tomasgard, Asgeir; Barton, Paul I
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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.
Computational Management Science
Springer Berlin Heidelberg
Hellemo, Lars et al. “Decision-Dependent Probabilities in Stochastic Programs with Recourse.” Computational Management Science (August 2018): 1-27 © 2018 The Author(s)
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