The sustainable hybrid truck-drone delivery model with stochastic customer existence

Drone delivery is a fast delivery mode that has gained tremendous attention from academia and various companies in recent years. However, due to limited battery and payload capacities which may reduce the system's efficiency, it is better to coordinate ground vehicles and drones to take advantage of both trucks' large capacity and the drone's high speed. As a restriction for realistic parcel delivery systems, customer presence is only sometimes deterministic. For instance, a customer makes an order from an e-retailer, but due to various probable reasons, he cannot be present at home to get service. In this paper, we have introduced a sustainable hybrid truck-drone delivery model with stochastic customer presence. We have modeled the system with the Markov chain and proposed a linear mathematical model. This work processes with a heuristic and a Branch-and-Bound algorithm. Also, we have carried out numerous computational experiments to evaluate the proposed solution methods' performance, where the results show the efficiency of the proposed algorithms. Finally, we performed a detailed sensitivity analysis on a case study and studied various aspects of the problem. The results highlight that truck and drone coordination reduces completion time, operational costs, truck emissions, and social penalties.