Optimization of subway freight compartment configuration and loading based on flexible time windows
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摘要: 为缓解城市道路拥堵，提高城市物流系统周转效率，提出了利用地铁线路在非高峰时段开展货物运输；基于客货共载运输模式，在满足乘客出行需求的前提下，推算了各列车最多可挂载的货物车厢数，在此基础上进行货物车厢配置与装载方案优化；以列车货物车厢配置计划与货物装载分配方案为决策变量，考虑货物送达柔性时间窗与容量限制的约束条件，以配送服务惩罚和货物车厢挂载成本最低为目标，构建了整数线性规划模型，并利用CPLEX优化软件进行模型求解。试验结果表明：为满足4类不同送达时限货物运输需求，方案共配置货运车厢42节，运营总成本为16 970元；随着延迟送达惩罚系数增大，货物延迟送达率呈快速降低趋势，当延迟送达惩罚系数由5元·h-1增加到100元·h-1时，延迟送达率由22.50%降至8.75%，随着提前送达惩罚系数增大，货物提前送达率同样呈现快速降低趋势，当提前送达惩罚系数由0增加到40元·h-1时，提前送达率由37.50%降低至3.75%，说明构建的模型对货物服务时效反应较为灵敏，同时有效满足货物送达服务时限要求；当某类货物惩罚系数增加时，该货物送达的提前率或延迟率会降低，整体表现为货物送达的准点率提高，服务水平得到改善，说明优化模型对不同类型货物的送达惩罚系数反应较为敏感；随着客运满载系数的增大，货物送达的准点率呈现递增趋势，货物送达提前率与延迟率总体上呈下降趋势，方案运营总成本也呈递减趋势，说明适当提高客运满载率阈值可以缓解部分列车运力，进而提高货物送达的准点率。Abstract: 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.
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表 1 货物送达时限需求量
Table 1. Delivery time requirements for freights
货物种类 A B C D 货物编号 1~24 25~44 45~61 62~80 货物总质量/kg 66 176 51 331 44 487 43 554 送达时限 9:40~9:55 10:25~10:35 11:00~11:12 9:00~12:00 
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表 2 不同服务惩罚的总成本
Table 2. Total costs of different service penalties
惩罚系数/(元·h-1) 提前送达率/% 延迟送达率/% 总成本/ 元 计算时间/ s M1, w M2, w 0 20 37.50 11.25 16 886 71 5 20 20.00 10.00 16 929 245 10 20 17.50 11.25 16 970 731 20 20 7.50 18.75 17 032 1 627 40 20 3.75 23.75 17 047 209 10 5 37.50 22.50 16 862 376 10 20 17.50 11.25 16 970 731 10 40 18.75 10.00 17 058 383 10 80 20.00 10.00 17 232 101 10 100 22.50 8.75 17 319 301
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表 3 不同客运满载率的总成本
Table 3. Total costs of different passenger load factors
θ 延迟送达率/% 提前送达率/% 总成本/元 计算时间/s 0.4 15.00 23.75 17 253 1 139 0.5 11.25 17.50 16 970 731 0.6 11.25 16.25 16 957 391 0.7 8.75 15.00 16 952 457 0.8 7.50 15.00 16 648 532
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表 4 不同送达时限要求的总成本
Table 4. Total costs of different delivery time requirements
案例 惩罚系数/(元·h-1) 延迟送达率/% 提前送达率/% 总成本/元 计算时间/s A B C D A B C D 1 M1, A=10, M2, A=20 33.3 0 5.9 0 4.2 30 52.9 0 16 970 731 2 M1, A=20, M2, A=40 29.2 0 5.9 0 4.2 25 52.9 0 17 065 566 3 M1, A=60, M2, A=100 29.2 0 5.9 0 0.0 25 52.9 0 17 354 369 4 M1, B=10, M2, B=20 33.3 0 5.9 0 4.2 30 52.9 0 16 970 731 5 M1, B=20, M2, B=40 29.2 0 5.9 0 4.2 20 52.9 0 16 982 458 6 M1, B=60, M2, B=100 37.5 0 5.9 0 4.2 10 76.5 0 16 999 554 7 M1, C=10, M2, C=20 33.3 0 5.9 0 4.2 30 52.9 0 16 970 731 8 M1, C=20, M2, C =40 33.3 5 5.9 0 4.2 10 35.3 0 16 997 697 9 M1, C=60, M2, C =100 33.3 10 5.9 0 4.2 40 11.8 0 17 007 162 10 M1, D=10, M2, D=20 33.3 0 5.9 0 4.2 30 52.9 0 16 970 731 11 M1, D=20, M2, D =40 33.3 0 5.9 0 4.2 30 52.9 0 16 970 731 12 M1, D=60, M2, D =100 33.3 0 5.9 0 4.2 30 52.9 0 16 970 731
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