Covering Routing Problem with Robots and Parcel Lockers: A Sustainable Last-Mile Delivery Approach

Abstract

This study presents the Covering Routing Problem with Robots and Parcel Lockers (CRP-R-PL), a challenge arising in sustainable last-mile delivery contexts such as e-commerce and city distribution. In this problem, trucks depart from a central depot, delivering parcels directly to a subset of customers or a subset of parcel lockers. With these parcel lockers, the remaining customers could pick up items if they prefer the pick-up delivery method. In addition, each truck is equipped with an electric-powered Sidewalk Autonomous Delivery Robot (SADR), a sustainable delivery solution used in the U.S. and Canada by Uber and Amazon. This zero-emission vehicle is deployed to get off the truck, serve one or multiple customers, and then return to the same truck for battery swap and package retrieval. For the routing of SADRs, the trucks act as a moveable satellite depot to serve the remaining customers. The CRP-R-PL seeks cost-minimizing solutions by determining optimal parcel locker locations and routes of trucks and SADRs to serve all customers. We offer a mixed-integer programming formulation and a greedy heuristic to solve it. The CRP-R-PL includes three decisions: 1) finding the location of parcel lockers, 2) routing the trucks to visit the customers and parcel lockers, and 3) routing the SADRs to serve the remaining customers. Since this problem has yet to be studied in the literature, a new set of benchmark instances is introduced for the CRP-R-PL and solved by Gurobi alongside the parameter's sensitivity analysis.