A stochastic-fuzzy multi-objective model for the last-mile delivery problem using drones and ground vehicles, a case study

Drone delivery as a novel approach for parcel delivery has been under the focus of many scholars and practitioners. In this regard, this paper introduces a stochastic-fuzzy multi-objective optimization model for designing a last-mile delivery system with drones and ground vehicles. The first two objective functions aim to minimize the detrimental effects of the delivery system on the environment and the total costs. The last objective function maximized the system’s reliability by considering the breakdown probability of both drones and ground vehicles. Then, AUGMECON2 is utilized as an exact method to solve the proposed model. besides determining the number of required drones and ground vehicles, the model indicates locations and capacities of facilities where vehicles start their one-to-one trips to meet the customer demands. The proposed model is then validated by applying it to a real case study of an e-commerce company in Karaj, Iran. The findings suggest that the system’s total cost rises when the reliability increases and the environmental impacts decrease. Furthermore, when both drones and ground vehicles are considered for meeting the customer demands, the delivery system functions better in terms of costs, environmental impacts, and reliability than when only one mode of delivery is considered.