New algorithmic framework for conditional value at risk: Application to stochastic fixed-charge transportation

Description

This paper introduces a new algorithmic scheme for two-stage stochastic mixed-integer programming assuming a risk averse decision maker. The focus is the minimization of the conditional value at risk for a hard combinatorial optimization problem. Some properties of a mixed-integer non-linear programming formulation for conditional value at risk are studied as well as their algorithmic implications. This yields to a procedure for obtaining lower and upper bounds on the optimal value of the problem that may lead to an optimal solution. The new developments are applied to a fixed-charge transportation problem with stochastic demand, and they are computationally tested. The corresponding results are thoroughly presented and discussed.

Abstract

Ministerio de Economía y Competitividad MTM2015-63779-R

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Ministerio de Economía y Competitividad MTM2016-74983-C02-01

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Fundação para a Ciência e Tecnologia UID/MAT/04561/2013

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