A granular iterated local search for the asymmetric single truck and trailer routing problem with satellite depots at DHL Group

To plan the postal deliveries of our industry partner DHL Group (DHL), the single truck and trailer routing problem with satellite depots (STTRPSD) is solved to optimize mail carriers routes. In this application context, instances feature a high number of customers and satellites, and they are based on real street networks. This motivates the study of the asymmetric STTRPSD (ASTTRPSD). The heuristic solution methods proposed in the literature for the STTRPSD can either solve only the symmetric problem variant, or it is unclear whether they can also be used to solve the ASTTRPSD. We introduce an iterated local search, called ILS-ASTTRPSD, which generates different first-level tours in the perturbation phase, and improves the second-level tours in the local search phase. To speed up the search, granular neighborhoods are used. The computational results on instances from the literature prove the capability of ILS-ASTTRPSD to return high-quality solutions. On DHL instances, ILS-ASTTRPSD significantly decreases total travel times of the mail carriers and returns solutions with a different structure compared to the ones provided by DHL. Based on these differences, we give recommendations on how DHL could design more efficient mail carrier practices. Dedicated computational experiments reveal that considering parking and loading times when solving the ASTTRPSD leads to lower travel times, and that ignoring parking times is more counterproductive than ignoring loading times. Moreover, we assess the robustness of our solutions under parking time fluctuations. Finally, we derive properties of instances for which optimal solutions contain multiple second-level tours rooted at the same parking spot and for which the optimal solutions of the ASTTRPSD correspond to the ones of a pure traveling salesman problem.