A location-routing problem for local supply chains

This study addresses a local Supply Chain problem by proposing the Collection and Delivery Location Open Routing Problem (CDLORP), a variant of the classical location-routing problem that considers both collection and distribution routes to decide where to locate facilities. Collection routes are responsible for picking up the required raw material from local suppliers, while distribution routes deliver the final product to local customers. This study is motivated by a public initiative that desires to seize the by-product generated by the agro-industrial local sector to produce and provide healthy and nutritional snacks to students in the public elementary school system in Saltillo, Coahuila, Mexico. A node-based formulation and a flow-based formulation are proposed to solve instances of the problem. The formulations are valid for the symmetric and asymmetric cases of the problem. Four families of valid inequalities from the literature are adapted for the problem and are used to implement two branch-and-cut algorithms based on the proposed formulations. Computational experiments using 42 benchmark instances of different sizes (25 to 260 vertices) are performed to assess the efficacy of the proposed formulations and algorithms. The best results are obtained by the branch-and-cut algorithm using the node-based formulation. Finally, a case study is also addressed and optimally solved with the branch-and-cut algorithm using the node-based formulation. The results obtained for the benchmark instances and the case study show that the proposed approach can solve real-life problems to develop local supply chains for new products.