The stochastic location model with risk pooling

The Location Model with Risk Pooling (LRMP) seeks to locate distribution centers to minimize the sum of fixed location costs, transportation costs, and inventory costs. The risk-pooling effects of consolidating inventory sites are explicitly handled in the location model. In this paper, we present a stochastic version of the LMRP (SLMRP) that optimizes location, inventory, and allocation decisions under random parameters described by discrete scenarios. The goal is to find solutions that minimize the expected cost of the system across all scenarios. The SLRMP framework can also be used to solve multi-commodity and multi-period problems. We present a Lagrangian-relaxation–based exact algorithm for the SLMRP. The Lagrangian sub-problem is a non-linear integer program, but it can be solved by a low-order polynomial algorithm. We discuss simple variable-fixing routines that can drastically reduce the size of the problem. We present quantitative and qualitative computational results on problems with up This research was supportd by NSF Grants DMI-9634750 and DMI-9812915. This support is gratefully acknowledged.