Highlights • A new application, termed Vehicle Routing Problems with Drones Equipped with Multi-Package Payload Compartments (VRP-D-MC), is studied. • A novel adaptive multi-start simulated annealing meta-heuristic algorithm is proposed to solve large-scale instances. • The proposed algorithm is competitive with state-of-the-art algorithms in terms of solution quality. • An analysis of the experimental results offers managerial insights into drone delivery operations.

Abstract The vehicle routing problem with drones (VRP-D) consists of designing combined truck-drone routes and schedules to serve a set of customers with specific requests and time constraints. In this paper, VRP-D is extended to include a fleet of drones equipped with multi-package payload compartments to serve more customers on a single trip. Moreover, a drone can return to a truck, different from the one from which it started, to swap its depleted battery and/or to pick up more packages. This problem, denoted as VRP-D equipped with multi-package payload compartments (VRP-D-MC), aims to maximize total profit. In this work, an adaptive multi-start simulated annealing (AMS-SA) metaheuristic algorithm is proposed to efficiently solve this problem. Experimental results show that the proposed algorithm outperforms the current state-of-the-art algorithms for VRP-D in terms of solution quality. Extensive analyses have been conducted to provide managerial insights. The analyses carried out show ($i$) the benefits of using drones equipped with different compartment configurations, ($\mathrm{ii}$) the incremental total profit obtainable using a combined truck-drone fleet rather than a fleet of trucks, ($\mathrm{iii}$) the benefit of swapping drone battery while picking up the items to deliver, and ($\mathrm{iv}$) the impact of the packages load on the consumption energy of battery drone. It is also demonstrated that the different intensification and diversification mechanisms adopted improve the convergence of the traditional SA.