Last-mile delivery made practical

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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 k LMD, 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 k LMD 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.