A location-inventory model for large three-level supply chains

We study the location-inventory problem in three-level supply networks. Our model integrates three decisions: the distribution centers location, flows allocation, and shipment sizes. We propose a nonlinear continuous formulation, including transportation, fixed, handling and holding costs, which decomposes into a closed-form equation and a linear program when the DC flows are fixed. We thus develop an iterative heuristic that estimates the DC flows a priori, solves the linear program, and then improves the DC flow estimations. Extensive numerical experiments show that the approach can design large supply networks both effectively and efficiently, and a case study is discussed.

► Our approach allows to design large supply networks with general features.
► Our continuous model integrates location, allocation as well as inventory decisions.
► At each iteration of our heuristic, we fix the DC flows and solve a linear program.
► The heuristic is able to reveal the benefits resulting from inventory decisions.
► The approach is inspired by and illustrated on a real case.