A fast simulated annealing heuristic for the multi-depot two-echelon vehicle routing problem with delivery options

We studied a variant of the vehicle routing problem (VRP) arising in last-mile distribution, called the multi-depot two-echelon vehicle routing problem with delivery options (MDTEVRP-DO). The MDTEVRP-DO involves two decision levels: (i) designing routes for a fleet of vehicles located in multiple depots to transport customer demands to a set of satellites and (ii) routing a fleet of vehicles from the satellites to serve the final customers. Nowadays, a relevant feature of the problem characterizing delivery services is that customers can collect their packages at pickup stations near their homes or workplaces. We designed an effectively simulated annealing (SA) heuristic for the problem. The new algorithm was extensively tested on benchmark instances from the literature, and its results were compared with those of start-of-the-art algorithms. The results show that the proposed SA obtains 30 out of the 36 best solutions for the MDTEVRP-DO benchmark instances. Moreover, its computation performance is superior to state-of-the-art algorithms for the MDTEVRP-DO.