Decision-dependent probabilities in stochastic programs with recourse

作者：Lars Hellemo, Paul I. Barton, Asgeir Tomasgård · 发表于：Computational Management Science · 年份：2018 · DOI：10.1007/s10287-018-0330-0 · 被引用次数：116 · 研究领域：Risk and Portfolio Optimization、Optimization and Mathematical Programming、Supply Chain and Inventory Management

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.