A three-phase algorithm for the three-dimensional loading vehicle routing problem with split pickups and time windows

Abstract

In a survey of Belgian logistics service providers, the efficiency of first-mile pickup operations was identified as a key area for improvement, given the increasing number of returns in e-commerce, which has a significant impact on traffic congestion, carbon emissions, energy consumption and operational costs. However, the complexity of first-mile pickup operations, resulting from the small number of parcels to be collected at each pickup location, customer time windows, and the need to efficiently accommodate the highly heterogeneous cargo inside the vans, has hindered the development of real-world solution approaches. This article tackles this operational problem as a vehicle routing problem with time windows, time-dependent travel durations, and split pickups and integrates practical 3D container loading constraints such as vertical and horizontal stability as well as a more realistic reachability constraint to replace the classical “Last In First Out” (LIFO) constraint. To solve it, we propose a three-phase heuristic based on a savings constructive heuristic, an extreme point concept for the loading aspect and a General Variable Neighborhood Search as an improvement phase for both routing and packing. Numerical experiments are conducted to assess the performance of the algorithm on benchmark instances and new instances are tested to validate the positive managerial impacts on cost when allowing split pickups and on driver working duration when extending customer time windows. In addition, we show the impacts of considering the reachability constraint on cost and of the variation of speed during peak hours on schedule feasibility.