A two-echelon inventory-location problem with service considerations

We study the problem of designing a two-echelon spare parts inventory system consisting of a central plant and a number of service centers each serving a set of customers with stochastic demand. Processing and storage capacities at both levels of facilities are limited. The manufacturing process is modeled as a queuing system at the plant. The goal is to optimize the base-stock levels at both echelons, the location of service centers, and the allocation of customers to centers simultaneously, subject to service constraints. A mixed integer nonlinear programming model (MINLP) is formulated to minimize the total expected cost of the system. The problem is NP-hard and a Lagrangian heuristic is proposed. We present computational results and discuss the trade-off between cost and service.