A novel mathematical model and a hybrid grouping evolution strategy algorithm for an automated last mile delivery system considering wind effect

Efficient and timely delivery of goods in last-mile logistics is a key challenge for e-commerce companies. With the rise of drone technology, drone-based delivery has emerged as a promising solution to address the challenges of traditional last-mile logistics. In light of the environmental and social challenges faced by last-mile delivery, integrating sustainability into logistics planning has become a vital requirement rather than a mere option. Drones have been identified as a potential solution to reduce greenhouse gas emissions and improve the sustainability of last-mile logistics. In this study, we present a mathematical model for the multi-depot multi-period drone delivery problem, which considers wind patterns and multi-periodicity to optimize the routing of multiple drones from multiple depots over a planning horizon of one day or shift. We included the wind profiles in our modeling to achieve a more realistic drone route planning. To address the complexity of the problem, we employ the Dantzig-Wolfe decomposition method to obtain a lower bound for the problem. Since we have a grouping problem, a novel metaheuristic algorithm, based on a grouping evolution strategy algorithm is developed for efficient drone routing. The algorithm uses the structural information along with the problem with the aid of a proposed constructive heuristic based on the well-known best fit strategy. Results show that proposed approach, achieved a solution with a gap of 2.99% to the lower bound on average, demonstrating its effectiveness in addressing the complexity of the multi-depot multi-period drone delivery problem while considering the impact of wind patterns.