A conceptually simple algorithm for the capacitated location-routing problem

Location-routing problems (LRPs) jointly optimize the location of depots and the routing of vehicles. The most studied LRP variant, the capacitated LRP (CLRP), has been addressed by a large number of metaheuristic approaches. These methods often decompose the problem into a location stage to determine a promising depot configuration and a routing stage, in which a vehicle-routing problem is solved to assess the quality of the previously determined depot configuration. Unfortunately, the CLRP literature does not shed much light on the important question which algorithmic features have the biggest influence on the solution quality and runtime of such heuristics. The purpose of this paper is to propose a conceptually simple (yet reasonably effective) heuristic for the CLRP and to provide some insights on the design of successful metaheuristics for this problem. Our algorithm is a hybrid combining (i) a GRASP phase that uses a variable neighborhood descent for local improvement in the location stage, and (ii) a variable neighborhood search in the routing stage. We analyze the impact of the algorithmic components on solution quality and runtime. In addition, we find that the suboptimal routing solutions used to assess the quality of the investigated depot configurations in tendency lead to depot configurations with too many open depots. We propose a depot configuration refinement phase that alleviates this drawback, and we show that this algorithmic component significantly contributes to the solution quality of our method, enabling it to provide reasonable results in comparison to the state-of-the-art methods from the literature.