Grasp with Learning Process for a Two-echelon Location Routing Problem

This article concerns a problem still seldom studied, the two-echelon or two-level vehicle routing problem (LRP-2E). It is raised by distribution or collection networks involving two sets of vehicle trips: first-level trips serve from a main depot a set of satellite depots, which must be located, while second-level trips visit customers from these satellites. After a literature review on the LRP-2E and its variants, the paper describes four constructive heuristics and one meta-heuristic to solve the LRP-2E with capacity constraints on vehicles and satellites. The best heuristic builds giant tours over the set of customers, each tour being limited by the capacity of a first-level vehicle. The giant tours are then partitioned using a splitting procedure which inserts the satellite depots. A TSP is finally solved to visit the satellites selected. The proposed meta-heuristic is a greedy randomized adaptive search procedure (GRASP) reinforced by a learning process. The results show that our GRASP clearly outperforms the constructive heuristics. Furthermore, it is competitive with the best meta-heuristic published for the single-echelon LRP.