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Decision-dependent probabilities in stochastic programs with recourse

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.
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Category

Academic article

Language

English

Author(s)

Affiliation

  • SINTEF Industry / Sustainable Energy Technology
  • Norwegian University of Science and Technology
  • Massachusetts Institute of Technology (MIT)

Year

2018

Published in

Computational Management Science

ISSN

1619-697X

Volume

15

Issue

3-4

Page(s)

369 - 395

View this publication at Norwegian Research Information Repository