An algorithm for flexible transshipments with perfect synchronization

Abstract

Direct and instant deliveries have gained popularity among customers, but have also increased the burden on cities due to rising transport incidents, especially as delivery vehicles often drive empty when returning to their origin. Flexible transshipments with perfect synchronization would allow loads to be transshiped between these vehicles without the need for storage facilities. This may increase their average proximity to their origin and reduce the proportion of empty rides. We present a problem-specific algorithm with three sub-steps to solve this concept. The first evaluates the relational position between two deliveries and, based on 36 structured cases, decides which pairs to exclude from the solution space. The second formulates the optimization problem to find the best transshipment location while considering time-limit constraints and transfer times. Finally, we apply the request-pair combination problem to graph theory to determine the lowest overall travel time. In our paper, we consider a continuous problem definition which allows flexible transshipments, and assume unit-sized capacity per vehicle and a maximum of one transshipment per request.We show that our algorithm reduces the initial total travel time of direct deliveries by 9.6% in a numerical simulation, and by 11% in a case study using food delivery data from the city of Bordeaux. We also demonstrate that the total time is best reduced by increasing time constraints rather than adding requests to increase the chance of transshipments. Our algorithm not only helps to reduce travel time, but also improves sustainability, mitigates driver shortages and is easy to implement.