The high population density in metropolitan areas, high-rise buildings, and changes in people's lifestyles have completely changed the way postal packages are delivered. People no longer go to the ground floor to receive a postal package. In the meantime, the delivery of postal packages through the balconies and windows of the units on the upper floors of the buildings will gradually become inevitable. Hence, a new Vehicle Routing Problem with Drone mathematical model has been developed with the objective of minimizing total delivery time and with the ability to deliver postal packages in the path of drones at different heights. In addition, the drone's energy consumption is computed by taking into account wind speed, the weight of the postal parcel, the weight of the drone's body, and other factors in the drone's path. A two-phase algorithm based on the nearest neighborhood and local search is presented to solve the developed mathematical model in different instances. Several small-sized test problems are designed and solved, and the performance of the heuristic approach is evaluated compared to the outputs of the CPLEX solver. Finally, the proposed model is implemented on a real-world scale to demonstrate the efficacy and applicability of the proposed model as well as the heuristic approach. The results show that the model successfully finds the optimal planning of the delivery routes, especially when we deal with delivery points at different heights.
Keywords: Drone; Energy consumption; Height consideration; Heuristic; Parcel delivery; UAV; VRPD.
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