A Branch-and-Price Algorithm for Optimal Routing of Delivery Robots

Abstract

Increasing parcel volumes, environmental challenges, and customer expectations have made innovative delivery concepts for last-mile logistics essential in recent years. Autonomous delivery vehicles such as delivery robots or drones are tested worldwide. In this work, we examine the use of electrical delivery robots to optimize a last-mile network. The network consists of a fleet of homogeneous single-unit capacity robots, depots equipped with recharging stations, and customers. Each customers is defined by a time window and a profit. The goal is to find a set of tours that maximizes the total collected profit. These tours have to respect the customers' time windows and battery constraints of the robots. We present a branch-and-price algorithm to solve this combinatorial optimization problem exactly. Within this algorithm, the problem of finding feasible tours arises. To decide on the feasibility of a tour, we present a polynomial dynamic program and prove its correctness. The computational studies on modified benchmark instances show that the algorithm can solve instances that have realistic time window lengths and up to 144 customers in a reasonable time.