Decision-dependent probabilities in stochastic programs with recourse |
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Authors: | Lars Hellemo Paul I Barton Asgeir Tomasgard |
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Institution: | 1.Department of Economics and Technology Management,SINTEF Technology and Society,Trondheim,Norway;2.Process Systems Engineering Laboratory Department of Chemical Engineering,Massachusetts Institute of Technology,Cambridge,USA;3.Department of Industrial Economics and Technology Management,NTNU,Trondheim,Norway |
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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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