Expanding hub location-routing problem for hybrid hub-and-spoke multimodal transport network considering carbon emissions
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摘要: 针对现有多式联运网络枢纽饱和度高、枢纽到城市直达运输成本高且效率低等不足，提出采用混合轴辐式多式联运网络研究扩增枢纽选址，同时优化运输线路；基于允许枢纽间转运和需求城市间巡回运输的运输网络，考虑低碳因素构建了最小化总运输成本、二级枢纽开放建设成本、枢纽处转运成本和总碳排放成本的数学模型，将问题分解为选址-分配与路径优化2个阶段，并针对两阶段特点分别采用0-1编码和数字编码设计了两阶段遗传算法；针对现有实际案例采用设计的算法进行求解，并将求得的最优运输方案与现实方案进行对比。研究结果表明：采用提出的算法进行10次运行获得的最优解与其平均值的差值百分比仅为4.7%，且平均求解时间仅为90.6 s；优化后网络扩增了2个枢纽，弃用了1个不合理枢纽，网络转运能力提高了11.3%，枢纽的平均饱和度降低了15.7%，不同枢纽的饱和度比原网络更均衡，不仅缓解了饱和枢纽的压力，还提高了空闲枢纽的周转率，从而提高了转运效率；优化后运输方案对应的总成本、运输成本、中转成本和碳排放成本分别降低了68.41%、68.14%、56.55%和86.76%，且碳排放减少最为突出。由此可见，提出的模型和算法对扩张轴辐式网络选址和混合轴辐式多式联运网络运输方案的组合优化具有较好的性能。Abstract: In view of the high hub saturation, as well as the high cost and low efficiency of direct transportation from a hub to cities of the existing multimodal transport network, a hybrid hub-and-spoke multimodal transport network was proposed to expand the hub locations and optimize the transportation routes. On the basis of the transport network allowing transfer between hubs and tours between cities and considering the low-carbon factors, a mathematical model was built to minimize costs including the total transportation cost, the construction cost to open secondary hubs, the transfer cost at hubs, and the total carbon emission cost. In this way, the problem was decomposed into two stages: the location-allocation and route optimization, and according to the characteristics of the two stages, a two-stage genetic algorithm using the 0-1 coding and digital coding was designed, respectively. The designed algorithm was applied to solve an existing real case, and the optimal transportation scheme obtained by the algorithm was compared with the actual scheme. Research results show that the difference percentage between the optimal solution and its average value obtained by 10 runs of the proposed algorithm is only 4.7%, and the average solution time is only 90.6 s. In the optimized network, two hubs are added, and an unreasonable hub is abandoned. The transfer capacity of the network improves by 11.3%, and the average saturation of hubs reduces by 15.7%. The saturations of different hubs are more balanced than that in the original network. The pressures of saturated hubs are relieved, and the turnover rates of idle hubs are raised to improve the transfer efficiency. The total cost, transportation cost, transfer cost, and carbon emission cost corresponding to the optimized transportation scheme reduce by 68.41%, 68.14%, 56.55%, and 86.76%, respectively, with the most prominent reduction in carbon emissions. It can be seen that the proposed model and algorithm have good performance in expanding the hub-and-spoke network locations and comprehensively optimizing the transportation scheme for the hybrid hub-and-spoke multimodal transport network. 7 tabs, 12 figs, 31 refs.
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图 7 全国物流大通道和节点布局示意
Figure 7. Schematic of layouts of national logistics channels and nodes
图 10 优化后多式联运网络运输方案
Figure 10. Transportation scheme of optimized multimodal transport network
图 11 优化后多式联运网络运输布局
Figure 11. Transportation layout of optimized multimodal transport network
图 12 原多式联运网络运输方案
Figure 12. Transportation scheme of original multimodal transport network
表 1 城市编号
Table 1. City numbers
编号 1 2 3 4 5 6 7 8 城市 宁波 重庆 成都 南昌 呼和浩特 北京 郑州 长沙 编号 9 10 11 12 13 14 15 16 城市 昆明 西安 兰州 乌鲁木齐 武汉 芜湖 蚌埠 徐州 
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表 2 规模经济折扣因子
Table 2. Discount factors of scale economy
不同枢纽 铁路运输 公路运输 一级枢纽与二级枢纽间 0.75 0.90 二级枢纽与二级枢纽间 0.75 0.90
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表 3 两阶段遗传算法10次运行结果
Table 3. Results of 10 runs by two-stage genetic algorithm
最优方案目标函数值/万元 最优总成本平均值/万元 差值百分比/% 计算时间/s 最优总成本 Z1 Z2 Z3 Z4 7.30×106 7.12×106 900 1.01×105 7.02×104 7.65×106 4.7 90.6
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表 4 案例最优解对应的二级枢纽选址及运输方案
Table 4. Optimal solutions of cases for locations and transportation schemes of secondary hub
开放为二级枢纽 运输路径方案 路段运输方式 已开放的枢纽：2、3、4 [1, 2] [1] [1, 2, 3] [1, 1] [1, 4] [1] 选择开放的枢纽：7、10 [1, 7, 5] [1, 1] [1, 7, 6] [1, 1] [1, 7] [1] [1, 8] [1] [1, 2, 9] [1, 1] [1, 10] [1] [1, 10, 11] [1, 1] [1, 10, 11, 12] [1, 1, 1] [1, 4, 13, 14] [1, 2, 2] [1, 4, 13] [1, 2] [1, 7, 16, 15] [1, 2, 2] [1, 7, 16] [1, 2]
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表 5 原网络流量分配
Table 5. Original network flow allocation
二级枢纽 一级枢纽至二级枢纽运输方式 一级枢纽至二级枢纽运量/104 t 运达需求城市 枢纽至需求城市运输方式 物资流量/104 t 重庆 公路 15 000 重庆 3 690 呼和浩特 铁路 1 772 郑州 铁路 3 449 长沙 铁路 2 073 昆明 铁路 1 940 西安 铁路 2 076 成都 公路 7 562 成都 3 011 西安 铁路 515 兰州 铁路 1 859 乌鲁木齐 铁路 1 885 徐州 铁路 292 南昌 2 025 南昌 公路 12 000 北京 铁路 1 856 武汉 公路 2 787 芜湖 公路 1 787 蚌埠 公路 1 910 徐州 铁路 1 635
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表 6 优化前后二级枢纽转运量对比
Table 6. Comparison of transfer volumes of secondary hubs before and after optimization
对比项 重庆 成都 南昌 郑州 西安 均值 枢纽容量/104 t 15 000 14 000 12 000 13 000 8 000 原实际转运量/104 t 15 000 7 562 12 000 原饱和度/% 100.00 54.01 100.00 84.67 优化后转运量/104 t 8 641 0 6 599 10 914 6 335 优化后饱和度/% 57.61 0 54.99 83.95 79.19 68.94
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表 7 两种网络运输方案成本对比
Table 7. Cost comparison of two network transporation schemes
成本类型 优化结果/万元 原网络结果/万元 差值百分比/% 总成本 7.30×106 2.31×107 68.41 运输成本 7.12×106 2.24×107 68.14 中转成本 1.01×105 2.32×105 56.55 二级枢纽开放成本 900 0 碳排放成本 7.02×104 2.299×105 86.76
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