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Decision-dependent probabilities in stochastic programs with recourse

Author

Listed:
  • Lars Hellemo

    (SINTEF Technology and Society)

  • Paul I. Barton

    (Massachusetts Institute of Technology)

  • Asgeir Tomasgard

    (NTNU)

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.

Suggested Citation

  • Lars Hellemo & Paul I. Barton & Asgeir Tomasgard, 2018. "Decision-dependent probabilities in stochastic programs with recourse," Computational Management Science, Springer, vol. 15(3), pages 369-395, October.
    • Handle: RePEc:spr:comgts:v:15:y:2018:i:3:d:10.1007_s10287-018-0330-0
    DOI: 10.1007/s10287-018-0330-0
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    References listed on IDEAS

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