Integrated location and inventory planning in service parts logistics with customer-based service levels

We analyze the integrated logistics network design and inventory stocking problem in service parts logistics, where each customer requires a certain response time-based service level. We introduce a non-linear mixed integer optimization model that explicitly captures the interdependency between network design (locating facilities, and allocating customers’ demands to facilities) and inventory stocking decisions (stock levels and their corresponding stochastic fill rates). We then provide two different linearized mixed integer formulations for this problem that can solve small and medium size problems. We show that it is still a challenging problem in general, for which we have a Lagrangian-relaxation based approach that provides extremely tight lower and upper bounds. Our extensive computational study shows the effectiveness of the proposed approach for a variety of problem instances, producing provably near-optimal integrated solutions.