Prize-collecting Electric Vehicle routing model for parcel delivery problem

Electric Vehicle (EV)-based parcel delivery is getting much more popular these days due to EVs being ecofriendly and sustainable. One well-known problem in the literature to study last-mile delivery via EVs is the Electric Vehicle Routing Problem (EVRP). One limitation of EVRP is that it assumes all customers must be visited directly by EVs. This forces companies to purchase or utilize additional EVs, increasing operational costs for EV utilization and routing. To overcome this limitation, the present work introduces the Prize- collecting EVRP with Time Windows (PC-EVRP-TW), utilizing multiple EVs for the home-delivery service of high-priority customers (customers with high loyalty or premium memberships), leaving the rest for the next day or outsourcing to a third-party shipper. It also ensures a minimum number of served demands to maintain service quality. PC-EVRP-TW is modeled by mixed-integer linear programming and solved by a problem-specific hybrid metaheuristic aiming to minimize EVs' route and usage cost and maximize collected profits (prizes) while satisfying EVs' load and battery capacity, task completion, and time window constraints. Analyses were performed on the optimal solution of PC-EVRP-TW. The results show that the company could achieve significant route cost savings, up to 22% compared to EVRP-TW. Additionally, remarkable reductions in EV usage costs, 6%, 16%, and 18%, were observed for various-size instances of PC-EVRP-TW. These findings highlight the potential for practitioners and managers to realize substantial cost savings and optimize EV usage by selectively serving a prioritized subset of customers daily, particularly when facing high utilization costs and the inability to serve all customers directly.