A new formulation approach for location routing-problems

A Location-Routing Problem (LRP) combines two difficult problems, facility location and vehicle routing, and as such it is inherently hard to solve. In this paper, we propose a different formulation approach than the common arc-based product-flow (Arc-BPF) approach in the literature. We associate product amounts to the nodes of the network resulting in a node-based product-flow (Node-BPF) formulation. Our main objective is to develop LRP models with fewer constraints and variables, which can be solved more efficiently. To introduce the proposed approach, we reformulate a complex four-index Arc-BPF LRP model from the literature as a three-index Node-BPF model, which computationally outperforms the former. We then introduce a heuristic method.