Joint Fleet Sizing and Routing for Multi-Truck–Multi-Drone Collaborative Delivery

Abstract

Truck–multi-drone collaborative delivery can reduce last-mile costs, but fleet sizing and routing are often optimized separately, making it difficult to match resources with demand under a delivery-period constraint. This study addresses the scenario of collaborative delivery involving multiple trucks and multiple drones by constructing a two-stage optimization framework that integrates fleet sizing and route planning. In the first stage, queueing models and continuous approximation are employed to determine the initial configuration of trucks and drones based on demand intensity and delivery cycle constraints. The second stage introduces continuous drone delivery and cross-vehicle retrieval to enhance the flexibility of truck–drone collaboration; while optimizing collaborative routes, the framework adjusts the allocation of trucks and drones—adding or reducing resources based on route feasibility and equipment utilization—thereby achieving the joint optimization of transport capacity and collaborative routes with the objective of minimizing total system costs. A node–resource–flow-separated three-chain encoding and an adaptive large neighborhood search–simulated annealing algorithm are designed to solve the model. Multi-scale numerical experiments show that, compared with four simplified fleet-sizing strategies, the proposed framework achieves average cost savings of 15.4–15.5% for medium- and large-scale instances. The results reveal an economic saturation point of the delivery period that shifts with node scale and a non-monotonic relationship between fleet size and coordination efficiency. The framework supports demand-driven fleet configuration and provides operational guidance for cost-effective truck–drone last-mile delivery.