Risk Management In Uncapacitated Facility Location Models Withrandom Demands

摘要

In this paper we consider a location-optimization problem where the classical uncapacitated facility location model is recast in a stochastic environment with several risk factors that make demand at each customer site probabilistic and correlated with demands at the other customer sites.Our primary contribution is to introduce a new solution methodology that adopts the mean-variance approach,borrowed from the finance literature,to optimize the "Value-at-Risk" (VaR) measure in a location problem.Specifically,the objective of locating the facilities is to maximize the lower limit of future earnings based on a stated confidence level.We derive a nonlinear integer program whose solution gives the optimal locations for the p facilities under the new objective.We design a branch-and-bound algorithm that utilizes a second-order cone program (SOCP) solver as a subroutine.We also provide computational results that show excellent solution times on small to medium sized problems.