2014-12-30Buch DOI: 10.18452/3068
Distribution shaping and scenario bundling for stochastic programs with endogenous uncertainty
Stochastic programs are usually formulated with probability distributions that are exogenously given. Modeling and solving problems with endogenous uncertainty, where decisions can influence the probabilities, has remained a largely unresolved challenge. In this paper we develop a new approach to handle decision-dependent probabilities based on the idea of distribution shaping. It uses a sequence of distributions, successively conditioned on the influencing decision variables, and characterizes these by linear inequalities. We demonstrate the approach on a pre-disaster planning problem of finding optimal investments to strengthen links in a transportation network, given that the links are subject to stochastic failure. Our new approach solves a recently considered instance of the Istanbul highway network to optimality within seconds, for which only approximate solutions had been known so far.
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