Multi-trip vehicle routing problem with order release time

This article studies a new variant of the vehicle routing problem known as the multi-trip vehicle routing problem with order release time. This problem frequently arises in the context of last-mile delivery in e-commerce. The order release time represents the time at which the customers’ goods become available at the depot for final distribution. Vehicles attached to the depot are used to perform multiple trips owing to the relatively short delivery distance. In this work, firstly, a mixed-integer linear programming (MILP) model is formulated. As the problem is a proven NP-hard problem, for solving large-sized instances quickly, an adaptive large neighbourhood search algorithm combined with a labelling procedure (ALNS-L) is proposed. The performance of the algorithm is further augmented by incorporating an optimal serving sequence property. The effectiveness of both the mathematical model and ALNS-L framework is verified by conducting extensive computational experiments on existing benchmark problems and real-life data.