Exact methods for two vehicle routing problems with lockers in last-mile delivery
摘要
Recent variants of Vehicle Routing Problems incorporate strategic delivery locations known as lockers, which can receive demands from various customers. In addition to the routing aspect, these problems consider the assignment of customers to lockers rather than requiring direct visits, leading to assignment costs associated with last-mile trips. The objective in these variants is to define routes and assignments so that every customer is either served directly at home or assigned to a locker, with the aim of minimizing the total traversal and assignment costs. This study examines two variants prevalent in the literature: the Vehicle Routing Problem with Lockers and Time Windows (VRPLTW) and the Vehicle Routing Problem with Private and Shared Delivery Locations (VRPPSDL). These problems differ in their consideration of factors such as time windows, vehicle capacity, and constant assignment costs. For VRPLTW, we propose and compare two Branch-and-Cut-and-Price (BCP) algorithms implemented within the VRPSolver framework. For VRPPSDL, we develop a specialized BCP algorithm based on the one proposed for VRPLTW. Computational experiments demonstrate the robustness of our procedures, which outperform the best exact methods available in the literature and achieve optimal solutions for several instances for the first time for both addressed problems.