Last-mile delivery made practical: an efficient route planning framework with theoretical guarantees

Last-mile delivery (LMD) refers to the movement of goods from transportation origins to the final destinations. It has widespread applications such as urban logistics, e-commerce, etc. One fundamental problem in last-mile delivery is route planning, which schedules multiple couriers' routes, i.e., sequences of origins and destinations of the requests under certain optimization objectives. Prior studies usually designed heuristic solutions to two strongly NP-hard optimization objectives: minimizing the makespan (i.e., maximum travel time) of couriers and total latency (i.e., waiting time) of requesters. There is no algorithm with theoretical guarantees for either optimization objective in practical cases. In this paper, we propose a theoretically guaranteed solution framework for both objectives. It achieves both approximation ratios of 6ρ, where ρ is the approximation ratio of a core operation, called kLMD, which plans for one courier a route consisting of k requests. Leveraging a spatial index called hierarchically separated tree, we further design an efficient approximation algorithm for kLMD with ρ = O(log n), where n is the number of requests. Experimental results show that our approach outperforms state-of-the-art methods by averagely 48.4%-96.0% and 49.7%-96.1% for both objectives. Especially in large-scale real datasets, our algorithm has 29.3x-108.9x shorter makespan and 20.2x-175.1x lower total latency than the state-of-the-art algorithms.