This work focuses on the optimization of a last-mile delivery system with multiple transportation modes. In this scenario, parcels need to be delivered to each customer point. The major feature of the problem is the combination of a fleet of road vehicles (vans) with a drone. Each van visits a subset of demand nodes to be determined according to the route of the van. The drone serves the customers not served by vans. At the same time, considering the safety, policy and terrain as well as the need to replace the battery, the drone needs to be transported by truck to the identified station along with the parcel. From each such station, the drone serves a subset of customers according to a direct assignment pattern, i.e., every time the drone is launched, it serves one demand node and returns to the station to collect another parcel. Similarly, the truck is used to transport the drone and cargo between stations. This is somewhat different from the research of other scholars. In terms of the joint distribution of the drone and road vehicle, most scholars will choose the combination of two transportation tools, while we use three. The drone and vans are responsible for distribution services, and the trucks are responsible for transporting the goods and drone to the station. The goal is to optimize the total delivery cost which includes the transportation costs for the vans and the delivery cost for the drone. A fixed cost is also considered for each drone parking site corresponding to the cost of positioning the drone and using the drone station. A discrete optimization model is presented for the problem in addition to a two-phase heuristic algorithm. The results of a series of computational tests performed to assess the applicability of the model and the efficiency of the heuristic are reported. The results obtained show that nearly 10% of the cost can be saved by combining the traditional delivery mode with the use of a drone and drone stations.

The outbreak of novel infectious diseases presents major public health challenges, highlighting the urgency of accelerating vaccination efforts to reduce morbidity and mortality. Vaccine allocation has become a crucial societal concern. This paper introduces a dynamic vaccine allocation model that considers demand uncertainty and vaccination willingness, focusing on the trade-off between fairness and efficiency. We develop a multi-period dynamic vaccine allocation model, evaluating optimal strategies over different periods. The model addresses structural differences among vaccination groups, strategy selection, dynamic demand, and vaccination willingness. Our findings suggest that prioritizing efficiency in the initial outbreak stages may lead to inequitable distribution, causing adverse social impacts, while overemphasizing fairness can undermine overall utility. Therefore, we propose a dynamic optimization-based strategy balancing fairness and efficiency at different pandemic stages. Our results indicate that allocation strategies should shift from efficiency to fairness as the pandemic evolves to enhance vaccine utility. Additionally, macro-level interventions like reducing free-rider behavior and increasing vaccination convenience can improve total vaccine utility. This study offers new perspectives and methodologies for dynamic vaccine allocation, highlighting the trade-off between fairness and efficiency, providing crucial insights for policy formulation and pandemic response.