Decision-dependent probabilities in stochastic programs with recourse

Lars Hellemo (), Paul I. Barton and Asgeir Tomasgard ()
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Lars Hellemo: SINTEF Technology and Society
Paul I. Barton: Massachusetts Institute of Technology
Asgeir Tomasgard: NTNU

Computational Management Science, 2018, vol. 15, issue 3, No 4, 369-395

Abstract: Abstract 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.

Date: 2018
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DOI: 10.1007/s10287-018-0330-0

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