Optimization of subway freight compartment configuration and loading based on flexible time windows

The utilization of subway lines for freight transportation during off-peak hours was suggested as a way to reduce the urban traffic congestion and enhance the turnover effectiveness of urban logistics systems. Based on the passenger and cargo co-load transportation mode, under the premise of meeting the travel needs of passengers, the maximum number of freight compartments that could be loaded on each train was calculated, and on this basis, the configuration and loading scheme of freight compartments was optimized. Train freight compartment configuration plan and freight loading allocation scheme were taken as decision variables. Considered the constraints of flexible time windows and capacity constraints for freight delivery, an integer linear programming model was constructed with the goal of minimizing delivery service penalties and freight compartment loading costs, and solved using CPLEX optimization software. Experimental results indicate that the scheme is configured with 42 freight compartments to meet the needs of 4 types of freight transportations with different delivery time limits, and the total operating cost is 16 970 yuan. As the penalty coefficient for delayed delivery increases, the rate of delayed delivery of freights decreases rapidly. When the penalty coefficient for delayed delivery increases from 5 yuan·h^-1 to 100 yuan·h^-1, the rate of delayed delivery decreases from 22.50% to 8.75%. As the penalty coefficient for advance delivery increases, the advance delivery rate of freights also shows a rapid decreasing trend. When the penalty coefficient for advance delivery increases from 0 to 40 yuan·h^-1, the advance delivery rate reduces from 37.50% to 3.75%. It indicates that the built model is sensitive to the time of freight delivery and can effectively meet the requirements of freight for service timeliness. When the penalty coefficient for a certain type of freight increases, the advance or delay rate of the freight delivery will decrease, showing that the overall performance of the on-time delivery of freights increases and the service level improves. This indicates that the optimization model is more sensitive to the penalty coefficients of delivery of different types of freights. As the passenger load factor increases, the on-time rate of freight delivery shows an increasing trend, the advance and delay rates of freight delivery show an overall decreasing trend, and the total operating cost of the scheme shows a decreasing trend. This indicates that increasing the passenger load factor threshold can alleviate the capacity constraints on certain trains and improve the on-time rate of freight delivery.