Taking logistics time, logistics cost, and carbon emissions as optimization objectives, air transportation is included in the cross-border logistics paths optimization of multimodal transportation. Considering the scale effect of transportation, a multiobjective optimization model of cross-border logistics paths including road, water, railway, and air is constructed. The problem of cross-border logistics paths along the “Belt and Road” regions for cities in inland is studied via the NSGA-II method. The research results show that Chengdu and Xi’an should bear a large number of cross-border air transportation and be constructed as the national airport-type logistics hub. The foreign destinations of cross-border air transportation are distributed in different regions, mainly in Eastern Europe and Eastern Central Europe. The optimization result shows that if there is a 1-fold increase in logistics cost, the logistics time can reduce by 1.37 folds after the cross-border air transportation joins in the model. Such a result has effectively guided the transition from cross-border water transportation to cross-border air transportation.

For the dynamic takeout delivery vehicle routing problem, which faces fluctuating order demand and time-varying speeds, this study presents a novel approach. We analyze the time distribution of takeout orders and apply a Receding Horizon Control (RHC) strategy to convert the dynamic challenge into a static one. The driving speed of delivery vehicles on different roads at different times is determined based on the subdivision criteria of the urban road network and a traffic congestion measurement method. We propose a dynamic takeout delivery vehicle routing optimization model and a time-varying subdivision road network is established to minimize the total delivery cost. We validated the model through simulation examples. The optimization results show that the total distribution cost is reduced after considering the time-varying subdivision road network, with the penalty cost decreasing by 39%. It is evident that considering the subdivision of the road network can enhance order delivery efficiency and optimize the overall dining experience. The sensitivity analysis of various parameters reveals that the delivery platform must appropriately determine the time domain and allocate the number of delivery personnel based on order scale to avoid escalating delivery costs. These findings provide theoretical guidance for vehicle routing planning in the context of delivery platforms.

In this paper, an output dynamic game model of intertwined supply chains operating in two different countries is established. The Nash equilibrium point of the model and its stable region are obtained using nonlinear dynamic principles. The complex properties of the system, such as stability, period-doubling bifurcations, and chaos, are investigated using numerical simulations. Our results suggest that the level of output and the system’s profits undergo bifurcation and chaos with an increase in the output adjustment speed. An interesting phenomenon occurs in that higher tariffs lead to the expansion of the stable range of the supply chain in the product-exporting country. The chaotic behavior of the system is sensitive to the value of the initial level of output. In supply chain competition, each supply chain firm should make suitable adjustments to the speed of output. To maintain the stability of domestic markets, excessive tariffs should be avoided. It is essential that each supply chain firm evaluates the potential impacts of different initial output values when making initial decisions. Using the method of delayed feedback control, the chaotic behavior of the system can effectively be controlled. These findings offer valuable and novel insight into inter-chain competition in supply chain networks.