The electric vehicle routing problem with time windows, partial recharges, and covering locations

Abstract

This research studies the electric vehicle routing problem with time windows, partial recharges, and covering locations (EVRPTW-PR-CL), as an extension of the electric vehicle routing problem with time windows and partial recharges (EVRPTW-PR), where covering locations (CLs) are facilities equipped with parcel lockers (PLs) and charging stations (CSs). The presence of PLs offers customers an alternative delivery option, where they are provided incentives to collect their parcels themselves, called self-pickup (SP) services. The objective is to seek routing plans that minimize the sum of travel costs, fixed operational costs for used EVs and CLs, and compensation paid to customers served by SP. To solve the problem, we derive a mixed-integer programming model and design an effective variable neighborhood search (VNS) algorithm coupled with problem-specific neighborhood operators, a dynamic programming procedure for optimal CS insertions, and a tailored set partitioning formulation (SPF) to enhance solution quality by utilizing collected routes so far. Numerical experiments are conducted on benchmark instances. VNS not only provides new best-known EVRPTW-PR solutions but also solves EVRPTW-PR-CL instances efficiently. Lastly, we present the effects of delivery options and compensation, offering insights that help decision makers design more sustainable and cost-effective last-mile delivery networks.