Hierarchical facility location-inventory-routing problem for maximal joint and gradual coverage

This paper introduces the Hierarchical Facility Location-Inventory-Routing Problem (HFLIRP) within a supply chain network design setting, involving both strategic and tactical level decisions. The strategic level considers locating distribution centers (DCs), locating and sizing retail branches (RBs), and determining DC–RB assignments. The tactical level addresses inventory routing for daily distributions. To tackle the HFLIRP, we first formulate a Mixed-Integer Non-Linear Programming (MINLP) model that aims to maximize the demand covered under the gradual coverage assumption, which also allows for the joint coverage of demand nodes by multiple facilities. Next, we propose a two-stage solution methodology that decomposes the problem into two sub-problems. The first sub-problem focuses on the strategic decisions of DC and RB locations and their assignments, utilizing a tangent line approximation (TLA) approach for linearization. The second sub-problem leverages the strategic decisions to minimize inventory routing costs, modeled as an Inventory Routing Problem (IRP). We carry out extensive numerical experiments to assess the performance of the two-stage solution approach against the original formulation across various problem instances. Our results demonstrate that the two-stage method is capable of achieving high-quality solutions within reasonable computational times.