Nature-inspired heuristics for the multiple-vehicle selective pickup and delivery problem under maximum profit and incentive fairness criteria

This work focuses on wide-scale freight transportation logistics motivated by the sharp increase of on-line shopping stores and the upsurge of Internet as the most frequently utilized selling channel during the last decade. This huge ecosystem of one-click-away catalogs has ultimately unleashed the need for efficient algorithms aimed at properly scheduling the underlying transportation resources in an efficient fashion, especially over the so-called last mile of the distribution chain. In this context the selective pickup and delivery problem focuses on determining the optimal subset of packets that should be picked from its origin city and delivered to their corresponding destination within a given time frame, often driven by the maximization of the total profit of the courier service company. This manuscript tackles a realistic variant of this problem where the transportation fleet is composed by more than one vehicle, which further complicates the selection of packets due to the subsequent need for coordinating the delivery service from the command center. In particular the addressed problem includes a second optimization metric aimed at reflecting a fair share of the net benefit among the company staff based on their driven distance. To efficiently solve this optimization problem, several nature-inspired metaheuristic solvers are analyzed and statistically compared to each other under different parameters of the problem setup. Finally, results obtained over a realistic scenario over the province of Bizkaia (Spain) using emulated data will be explored so as to shed light on the practical applicability of the analyzed heuristics.