In recent years, the energy consumption of vehicles has gained widespread attention due to the increasing importance of energy and environmental issues. Coupled with the explosive demand for vaccines that has spawned the massive deployment of refrigerated trucks, energy savings and efficiency improvement are the goals pursued by pharmaceutical logistics companies while getting the vaccine distribution task done. In order to evaluate the fuel consumption of refrigerated trucks during vaccine distribution, in this paper, we construct a mathematical model for the vehicle routing problem with time windows (VRPTW) for vaccine distribution with the aim of minimizing the total cost, including fossil fuel cost and penalty cost. Due to the NP-hardness and nonlinearity of the model, a genetic algorithm with a large neighborhood search operator (GA-LNS) and TSP-split encoding method is customized to address the large-scale problem. Numerical experiments show that the algorithm can obtain a near-optimal solution in an acceptable computational time. In addition, the proposed algorithm is implemented to evaluate a case of vaccine distribution in Haidian, Beijing, China. Insights on the effects of seasonal temperature, vehicle speed, driver working hours, and refrigeration efficiency are also presented.

In a public health emergency, residents urgently require a large number of rescue materials for treatment or protection. These rescue materials are usually located far from the emergency area. The government must organize rescue materials transportation by selecting suitable transport modes. Thus, we propose a material allocation model for public health emergencies under a multimodal transportation network to determine the best rescue material supply route. In this model, we set the demand priorities according to the emergency degrees to decide the transportation sequence. Meanwhile, we introduce the psychological pain cost brought by the rescue material shortage into the proposed model to trade off the priority and fairness of demand. Having compared it to the research literature, this is the first study that considers multiple categories of materials, absolute pain costs, relative pain costs and demand priority under multimodal transportation. The research problem is formulated into an integer programming model, and we develop a modified genetic algorithm to solve it. A set of numerical examples are conducted to test the performance of the proposed algorithm, and to investigate features and applications of the proposed model. The results indicate that the modified genetic algorithm performs better in the calculation examples at different scales. For small-scale instances, the algorithm produces consistent results with Gurobi. As the instance size increases, Gurobi fails to find the optimal solution within 1800 s, while this algorithm is able to find the optimal solution within an acceptable time frame. Additionally, when dealing with large-scale instances, the algorithm exhibits a significant advantage in terms of runtime. Sensitivity analysis of key factors indicate that (1) Adjusting the relative pain cost coefficient can make the best trade-off between fairness, economy and timeliness; (2) Compared with a single mode of transport, multimodal transport can reduce the psychological pain cost and the logistics cost; (3) Improving the loading and unloading capacity of nodes can reduce the delivery time of materials and the psychological pain cost of residents, but the influence of other factors and cost-effectiveness need to be considered.

With the development of sharing economy, a joint distribution mode has been increasingly adopted as the preferred cooperation mode of third-party logistics enterprises to achieve the efficient, resource-saving, and profit-optimal business goals of enterprises. In the joint distribution mode, the distribution price is one of key factors that influences the operation of the joint distribution. Thus, to acquire the optimal pricing for the logistics enterprises, we establish a pricing model based on dynamic game theory for a joint distribution system including one joint distribution company and two express enterprises. In the proposed model, two dimensions of games exist simultaneously, including the game between express competitors and the game between express and distribution enterprises. The multidimensional game leads to more complex system characteristics. Through the stability analysis, we find the Nash equilibrium point and its stability conditions. Numerical simulations are conducted to investigate the complex dynamical behaviors of the game model, such as the system stability region, the bifurcation diagram, the largest Lyapunov exponent, strange attractors, etc. The simulation results indicate that different price adjustment speeds and ranges have a significant impact on the system stability and the profits of all participants in the game. The parameter adjustment control can well dominate the chaotic behaviors of the system. Enterprises should make pricing decisions based on their market positions to promote the continuous and stable development of the operation mode of the multi-agent joint sharing distribution center.