Drone scheduling for parcel delivery with an access grade to stops on a fixed truck route

Abstract

In this paper, we consider a parcel delivery scheduling problem of minimizing the total duration for a truck-drone distribution system to serve a given set of customers. The single carrier truck plays the role of a mobile depot of multiple identical drones, and the drones with unit capacity perform the last-mile delivery from the carrier truck to each customer. An ordered set of truck stops for launching/retrieving drones is also given, and it constitutes a fixed route of the carrier truck. For the last-mile delivery of a drone to a customer, the launching stop and the retrieving stop of the drone must be the same. We newly introduce an integral parameter of access grade to an underlying parcel delivery model in order to obtain a flight time bound for each customer. By the flight time bound as a threshold, the given set of truck stops is partitioned into two disjoint subsets, namely sets of nearer stops and of farther stops. The carrier truck is required to choose a stop from the set of nearer stops for launching a drone to each customer. The access grade of nearer stops yields a generalized parcel delivery model, since it involves the case with a sufficiently large bound on the flight time as the underlying parcel delivery model with no access restriction to truck stops. In this paper, we first review an integer programming (IP) formulation of the underlying parcel delivery model, and then we modify it into the generalized version with the access grade of nearer stops. We also conduct numerical experiments to demonstrate the solution quality of the generalized version by utilizing an IP solver, and report the results.