Stochastic queue median over a finite discrete set

Many practical location decision problems require facility locations to be restricted to a finite set of points. Quite often such restrictions arise from natural constraints that are specific to the application setting. Motivated by such situations, this paper examines the Stochastic Queue Median (SQM) model of Berman, Larson and Chiu, where potential facility locations are restricted to a finite set of discrete points. An efficient algorithm is presented to solve for the optimal facility location parametrically in the systemwide arrival rate of calls. The complexity of the algorithm and a worst case analysis for the model formulation are also discussed.