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摘要: 以枢纽港船舶限制时间和支线船舶容量为基础, 分析了轴-辐式网络运输模式。以船舶最小总航行时间为目标函数, 建立了混合整数规划支线集装箱运输模型。通过设计巡回路线方法实现杂交和变异, 更新了解的构成, 运用遗传算法求解模型。计算结果表明: 当船舶容量为150 TEU时, 在160次迭代后, 总航行时间为708.6 h, 航线数量为8条; 当船舶容量分别为100、150 TEU时, 在150次迭代后, 总航行时间为714.6 h, 航线数量为9条; 对枢纽港船舶限制时间和支线船舶容量进行方差分析, F检验统计量的概率值均明显小于0.05;对支线船舶容量和运营成本进行敏感性分析, 增大船舶容量能够减小航线数量和运行时间, 但增大了运营成本, 增大枢纽港船舶限制时间能够减小航线数量; 考虑航行时间和运营成本, 当船舶容量为150 TEU时最合理。Abstract: On the basis of the limit time of hub port ship and branch ship capacity, hub-and-spoke network transportation model was analyzed. Taking the total minimum navigation time of ship as objective function, the mixed integer programming model of branch container transportation model was set up. Hybridization and variation were realized by designing itinerant route method, the structure of solution was updated, and genetic algorithm was used to solve the model. Calculation result indicates that when ship capacity is 150 TEU, the total navigation time is 708.6 h, and the route number is 8 after 160 times iteration. When the ship capacities are 100 and 150 TEU respectively, the total navigation time is 714.6 h, and the route number is 9 after 150 times iteration. Through the variance analysis of the limit time of hub port ship and branch ship capacity, the probability values of F test statistics are almost less than 0.05 significantly. Through the sensitivity analysis of branch ship capacity and running cost, while there is higher ship capacity, there are lower route number and navigation time, but there is higher running cost. When there is the bigger limit time of hub port ship, there is lower route number. While considering navigation time and running cost, the ship capacity of 150 TEU is most reasonable.
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表 1 港口的作业量和时间
Table 1. Working amouts and working times of ports
港口 卸箱量/TEU 装箱量/TEU 作业时间/h 限制时间/h 港口 卸箱量/TEU 装箱量/TEU 作业时间/h 限制时间/h 1南沙 0 0 0.0 0 16南伟 25 25 1.4 90 2盐田 20 25 1.2 80 17珠海 30 20 1.2 80 3惠州 21 27 0.8 80 18高栏 10 25 1.1 100 4新风 18 10 1.0 120 19斗门 20 16 1.0 110 5黄埔1 15 20 1.3 120 20阳江 25 21 1.0 200 6黄埔2 17 10 0.5 120 21水东 20 30 1.2 200 7增城 10 20 0.7 120 22海口 35 20 2.0 200 8太平 20 12 1.1 100 23湛江 20 28 1.0 200 9三山 15 25 1.2 110 24洋浦 10 20 0.9 200 10三水 15 22 1.0 140 25北海 20 21 1.4 200 11北滘 20 23 1.0 100 26防城 25 30 1.2 220 12容奇 15 9 1.0 100 27澳门 20 15 1.3 80 13江门 28 35 1.3 100 28蛇口 15 20 1.3 80 14中山 20 25 1.0 100 29新会 20 10 1.4 110 15三榕 15 20 1.3 140 30海防 15 22 1.2 220 注: 黄埔1和黄埔2分别为黄埔新港和黄埔旧港。 
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表 2 单船型情况下航线优化结果
Table 2. Route optimization result under one type of ship
航线 挂靠喂给港口 1 南沙—三山—新风—黄埔2—黄埔1—增城—南沙 2 南沙—高栏—新会—江门—南沙 3 南沙—珠海—澳门—阳江—南沙 4 南沙—三榕—三水—南沙 5 南沙—洋浦—北海—防城—海防—海口—湛江—水东—南沙 6 南沙—北滘—容奇—太平—南沙 7 南沙—斗门—中山—南伟—南沙 8 南沙—盐田—惠州—蛇口—南沙
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表 3 2种船型情况航线优化结果
Table 3. Route optimization result under two types of ships
航线 挂靠喂给港口 容量/TEU 1 南沙—斗门—江门—容奇—南沙 100 2 南沙—水东—阳江—高栏—南沙 100 3 南沙—海口—洋浦—南沙 100 4 南沙—中山—珠海—澳门—南沙 100 5 南沙—三水—北滘—黄埔2—增城—太平—南伟—南沙 150 6 南沙—新风—黄埔1—南沙 100 7 南沙—三山—三榕—新会—南沙 100 8 南沙—蛇口—盐田—惠州—南沙 100 9 南沙—湛江—防城—北海—海防—南沙 150
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表 4 不同约束条件下的总航行时间
Table 4. Total navigation times under different constraints
船舶容量/TEU 限制时间/h T1 T2 T3 T4 50 1 053.6 974.6 982.6 977.6 75 883.6 851.6 847.6 831.6 100 812.6 821.6 786.6 778.6 125 779.6 784.6 752.1 750.6 150 757.6 749.6 743.6 748.6 175 758.6 743.6 741.6 727.6 200 749.6 738.6 734.6 722.6 225 751.6 723.6 721.6 704.6 250 753.6 723.6 714.6 704.6
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表 5 方差分析结果
Table 5. Variance analysis result
h 差异源 平方和/h2 自由度 均方/h2 F统计量 概率 F临界值 受限制时间影响的因素 251 150.100 8 31 393.770 206.307 3.29×10-20 2.355 081 受船舶容量影响的因素 7 716.854 3 2 572.285 16.904 4.08×10-6 3.008 787 误差 3 652.083 24 152.170 总计 262 519.100 35
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表 6 航线数量、总航行时间和运营成本
Table 6. Route numbers, total navigation times and running costs
限制时间 船舶容量 航线数量/条 总航行时间/h 运营成本/千元 100 TEU 150 TEU 200 TEU 100 TEU 150 TEU 200 TEU 100 TEU 150 TEU 200 TEU T1 11 10 10 812 758 748 510 730 1 060 T2 10 9 8 820 750 739 520 728 1 040 T3 10 9 7 786 743 734 504 728 1 030 T4 8 7 6 779 750 721 500 730 1 010
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