Online Drone Scheduling for Last-mile Delivery

TL;DR

The paper addresses online last‑mile delivery using a hybrid truck–drone setup where requests arrive during a known truck route. It models drone assignment as interval coloring with a per‑color budget, employing online interval coloring to assign an idNumber and online bin packing to assign a binNumber, yielding $3$‑ and $2.7$‑competitive algorithms with $O(\log n)$ per‑request update time. It extends to online variable‑size drone scheduling (OVDS) with a $(2\alpha+1)$‑competitive solution and $O(n\log n)$ total time, where $\alpha$ is the battery ratio, and introduces an Interval Generator to map requests to delivery intervals using discrete truck stops. The results provide practical, provable guarantees for dynamically deploying drones in last‑mile logistics and offer a foundation for more sophisticated routing and recharging policies.

Abstract

Delivering a parcel from the distribution hub to the customer's doorstep is called the \textit{last-mile delivery} step in delivery logistics. In this paper, we study a hybrid {\it truck-drones} model for the last-mile delivery step, in which a truck moves on a predefined path carrying parcels and drones deliver the parcels. We define the \textsc{online drone scheduling} problem, where the truck moves in a predefined path, and the customer's requests appear online during the truck's movement. The objective is to schedule a drone associated with every request to minimize the number of drones used subject to the battery budget of the drones and compatibility of the schedules. We propose a 3-competitive deterministic algorithm using the next-fit strategy and 2.7-competitive algorithms using the first-fit strategy for the problem with $O(\log n)$ worst-case time complexity per request, where $n$ is the maximum number of active requests at any time. We also introduce \textsc{online variable-size drone scheduling} problem (OVDS). Here, we know all the customer's requests in advance; however, the drones with different battery capacities appear online. The objective is to schedule customers' requests for drones to minimize the number of drones used. We propose a $(2α+ 1)$-competitive algorithm for the OVDS problem with total running time $O(n \log n)$ for $n$ customer requests, where $α$ is the ratio of the maximum battery capacity to the minimum battery capacity of the drones. Finally, we address how to generate intervals corresponding to each customer request when there are discrete stopping points on the truck's route, from where the drone can fly and meet with the truck.

Figures (1)

• Figure 1: Above: The route of the truck is a straight line. The stops are given as black solid dots, the position $p$ of the truck is given as a blue square on the route and the request $q$ as a red square. Moreover, $S_i$ is the takeoff stop and $S_j$ is the landing stop and $I_{q}=[\ell_{q},r_{q}]$ is the corresponding interval of the solution. Below: The timeline of the day with the corresponding times $T_1,\cdots,T_k$ of the stops. $T_q$ is the position of the truck in the timeline when we receive the request $q$.

Theorems & Definitions (28)

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