A progressive filtering heuristic for the location-routing problem and variants

The location-routing problem (LRP) unites two important challenges in the design of distribution systems: planning the delivery of goods to customers (i.e., the routing of the delivery vehicles) and determining the locations of the depots from where these deliveries are executed. In this paper, we design an efficient and effective heuristic for the LRP based on an existing heuristic to solve the capacitated vehicle routing problem. Our heuristic reduces the solution space to a manageable size by the estimation of an upper bound for the number of open depots and then iteratively applies the routing heuristic on each remaining depot configuration. A progressive filtering framework, in which the vehicle routing problem is solved to a larger precision at each iteration, is employed to quickly detect unpromising configurations. Extensive experimentation reveals that the estimated upper bound effectively reduces the search space on different types of instances and that a good filtering design combines coarse and fine filters. Benchmarking shows that, despite its simple design, the final heuristic outperforms existing heuristics on the largest LRP benchmark set, on very-large-scale LRPs, and on 2-echelon LRPs. (C) 2020 Published by Elsevier Ltd.