Study on p-Robust Stochastic Facility Location Problem

Abstract

Snyder and Daskin presented p-robust models based on two classical facility location models, the PMP (P-median problem) and UFLP (uncapacitated facility location problem). We can impose a constraint dictating that the relative regret in any scenario must be no greater than p, where p>0 is an external parameter. In other words, the cost under each scenario must be within 100(1+p)% of the optimal cost for that scenario. For small p, there may be no p-robust solutions for a given problem. Thus, p-robustness adds a feasibility issue not present in most other robustness measures. In this paper, we use the following p-SPMP (p-robust stochastic P-median problem), p-SUFLP (p-robust stochastic uncapacitated facility location problem), p-SCPMP (p-robust stochastic capacitated P-median problem), p-SCFLP (p-robust stochastic capacitated facility location problem), p-SCPMPX (p-robust stochastic capacitated P-median problem, x is continuous) and p-SCFLPX (p-robust stochastic capacitated facility location problem, x is continuous) to analysis the stochastic facility location problems