A Scalable Last-Mile Delivery Service: From Simulation to Scaled Experiment

Abstract

In this paper, we investigate the problem of a last-mile delivery service that selects up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> available vehicles to deliver <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> packages from a centralized depot to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> delivery locations. The objective of the last-mile delivery service is to jointly maximize customer satisfaction (minimize delivery time) and minimize operating cost (minimize total travel time) by selecting the optimal number of vehicles to perform the deliveries. We model this as an assignment (vehicles to packages) and path planning (determining the delivery order and route) problem, which is equivalent to the NP-hard multiple traveling salesperson problem. We propose a scalable heuristic algorithm, which sacrifices some optimality to achieve a reasonable computational cost for a high number of packages. The algorithm combines hierarchical clustering with a greedy search. To validate our approach, we compare the results of our simulation to experiments in a 1:25 scale robotic testbed for future mobility systems.