The min-cost parallel drone scheduling vehicle routing problem

Adopting unmanned aerial vehicles (UAV), also known as drones, into the last-mile-delivery sector and having them work alongside trucks with the aim of improving service quality and reducing the transportation cost gives rise to a new class of Vehicle Routing Problems (VRPs). In this paper, we introduce a new optimization problem called the min-cost Parallel Drone Scheduling Vehicle Routing Problem (PDSVRP). This problem is a variant of the well-known Parallel Drone Scheduling Traveling Salesman Problem (PDSTSP) recently introduced in the literature in which we allow multiple trucks and consider the objective of minimizing the total transportation costs. We formulate the problem as a Mixed Integer Linear Program and then develop a Ruin and Recreate (R&R) algorithm. Exploiting PDSVRP solution characteristics in an effective manner, our heuristic manages to introduce “sufficient” rooms to a solution via new removal operators during the ruin phase. It is expected to enhance the possibilities for improving solutions later in the recreate phase. Multiple experiments on a new set of randomly generated instances confirm the performance of our approach. To explore the benefits of drone delivery as well as the insight into the impact of related factors on the contribution of drones’ use to operational cost, a sensitivity analysis is conducted. We also adapt the proposed algorithm to solve the PDSTSP and validate it via benchmarks available in the literature. It is shown that our algorithm outperforms state-of-the-art algorithms in terms of solution quality. Out of 90 considered instances, it finds 26 new best known solutions.