Applying NSGA-II to vehicle routing problem with drones considering makespan and carbon emission

Drones or unmanned aerial vehicles (UAV) are aerial vehicles capable of sustained flight independent of a human operator onboard. At present, many companies are developing their own delivery system with drones, in which the usage of drones in delivery is expected to develop substantially in the next few years. Although the speediness of drone delivery has been investigated, its feasibility remains in question and needs to be studied further. In addition, despite the advantages of using drones for delivery from an economic point of view, its environmental benefits must be tested. This study proposes the vehicle routing problem with drones (VRPD) model aimed at minimizing the makespan and carbon emissions of the delivery route. In this model, each truck is equipped with one drone to collaborate in delivery. In particular, this study aims to propose the mathematical formulation for the VRPD with two objectives—solve it with the non-dominated sorting genetic algorithm II (NSGA-II) and test the proposed algorithm with different-scale problems. Hypervolume and spacing are employed to check the quality of the solutions produced through the algorithm. The result shows that the algorithm can produce a remarkable result with good hypervolume and spacing values. The benefits of drones to reduce makespan and carbon emissions are tested through a significance test. Furthermore, this study finds that the difference when using drones is significant.