The two-echelon vehicle routing problem with covering options: City logistics with cargo bikes and parcel lockers

We introduce the two-echelon vehicle routing problem with covering options (2E-VRP-CO). This problem arises in sustainable applications for e-commerce and city distribution. In the first echelon, trucks depart from a single depot and transport goods to two types of locations. At covering locations, such as parcel lockers, customers can pick up goods themselves. At satellite locations, goods are transferred to zero-emission vehicles (such as cargo bikes) that deliver to customers. If desired, customers can indicate their choice for delivery. The 2E-VRP-CO aims at finding cost-minimizing solutions by selecting locations and routes to serve all customers. We present a compact mixed integer programming formulation and an efficient and tailored adaptive large neighborhood search heuristic that provides high-quality, and often optimal, solutions to the 2E-VRP-CO. The 2E-VRP-CO has as special cases the two-echelon vehicle routing problem, and the simultaneous facility location and vehicle routing problem without duration constraints. On these special cases, for which our heuristic predominantly solves the established benchmark instances either to optimality or to the best-known solution, our heuristic finds three new best-known solutions. Moreover, we introduce a new set of benchmark instances for the 2E-VRP-CO and provide managerial insights when distribution via both satellite and covering locations is most beneficial. Our results indicate that customers in the same area are best-served either via cargo-bikes or parcel lockers (i.e., not both), and that the use of parcel lockers has a great potential to reduce driving distance.