Optimal drone deployment for cost-effective and sustainable last-mile delivery operations

Delivery by drones holds significant potential to solve issues (such as high costs, access to remote areas, etc.) faced in last-mile delivery operations, particularly in the e-commerce industry. Still, it involves complex issues such as multi-trip operations, energy estimation, and battery recharge planning. A sound drone delivery problem entails an optimal drone deployment plan with routing details at the lowest possible cost. To this end, this study focuses on formulating a delivery problem that involves multi-trip drone routing, energy optimization, and travel time optimization problems where energy consumption by drones is modeled as a non-linear function. We develop a mixed integer non-linear programming model as an integrated optimization model. This model aims to: (a) maximize revenue by meeting demand completely without leaving idle drones, (b) optimize energy use by drones, and (c) minimize the required drone fleet size for an optimal plan. The proposed model is solved using the Gurobi Solver, which employs data supplied by a well-known e-commerce firm. We introduce a two-phase heuristic solution methodology to tackle larger networks' complexities. This method consists of the clustering phase (K-means clustering method) and the optimization phase. The robustness of the developed mathematical modeling is demonstrated by testing with varied large problem instances. The evaluation shows that expanding destination options boosts drone demand until saturation, necessitating more drones. Efficient route planning and fleet adjustments are crucial for meeting rising demand and satisfying customers amidst dense clustering. This model helps e-commerce manage daily last-mile drone deliveries and anticipate future growth.