中国管理科学 ›› 2025, Vol. 33 ›› Issue (5): 290-301.doi: 10.16381/j.cnki.issn1003-207x.2022.2318cstr: 32146.14/j.cnki.issn1003-207x.2022.2318
收稿日期:
2022-10-24
修回日期:
2023-12-28
出版日期:
2025-05-25
发布日期:
2025-06-04
通讯作者:
张令荣
E-mail:zhanglrm@dlut.edu.cn
基金资助:
Feng Wang, Lingrong Zhang(), Bo Lu
Received:
2022-10-24
Revised:
2023-12-28
Online:
2025-05-25
Published:
2025-06-04
Contact:
Lingrong Zhang
E-mail:zhanglrm@dlut.edu.cn
摘要:
基于“双碳”战略目标的提出和生鲜电商的迅速发展,本文研究了考虑碳排放的冷链物流多温共配问题,以车辆派遣成本、运输成本、制冷成本、碳排放成本及时间窗惩罚成本之和最小为目标建立混合整数规划模型。针对研究问题设计了一种两阶段启发式算法用于模型求解,利用时空距离对顾客进行聚类以改进初始解;依据问题特征设计邻域结构和邻域选择方式提高求解效率;采用自适应局部搜索避免陷入局部最优;引入重启策略和模拟退火算法的解接受规则增加解的丰富度。最后,通过不同规模的算例验证了算法的可行性,并从考虑时空距离、碳交易机制、多车厢车辆配送等角度进行分析,为企业和政府提供管理启示。
中图分类号:
王锋, 张令荣, 鲁渤. 考虑碳排放的冷链物流多温共配时变路径研究[J]. 中国管理科学, 2025, 33(5): 290-301.
Feng Wang, Lingrong Zhang, Bo Lu. Research on Time-varying Path of Multi-temperature Co-distribution in Cold Chain Logistics Considering Carbon Emissions[J]. Chinese Journal of Management Science, 2025, 33(5): 290-301.
表1
基于Solomon基准算例集的实验结果"
算例 | 本文算法 | 算例 | 本文算法 | ||||
---|---|---|---|---|---|---|---|
Gap | Gap | ||||||
R101 | 1044 | 1057.5 | 1.29% | R201 | 791.9 | 809.12 | 2.17% |
R102 | 909 | 913.9 | 0.54% | R202 | 698.5 | 714.19 | 2.25% |
R103 | 772.9 | 782.7 | 1.26% | R203 | 605.3 | 619.77 | 2.39% |
R104 | 625.4 | 632.3 | 1.10% | R204 | 506.4 | 515.394 | 1.78% |
C101 | 362.4 | 363.3 | 0.23% | C201 | 360.2 | 361.8 | 0.44% |
C102 | 361.4 | 362.2 | 0.21% | C202 | 360.2 | 361.8 | 0.44% |
C103 | 361.4 | 362.2 | 0.21% | C203 | 359.8 | 367.42 | 2.12% |
C104 | 358 | 358.9 | 0.25% | C204 | 350.1 | 356.77 | 1.91% |
RC101 | 944 | 959.0 | 1.59% | RC201 | 684.8 | 686.31 | 0.22% |
RC102 | 822.5 | 836.5 | 1.70% | RC202 | 613.6 | 615.04 | 0.23% |
RC103 | 710.9 | 714.7 | 0.53% | RC203 | 553.3 | 566.57 | 2.40% |
RC104 | 545.8 | 553.7 | 1.46% | RC204 | 444.2 | 455.3 | 2.50% |
表2
基于基准数据集的改造算例实验结果"
算例 | PSO[ | HPSO[ | 本文算法 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
最优解 | 最劣解 | 平均解 | 方差 | 最优解 | 最劣解 | 平均解 | 方差 | 最优解 | 最劣解 | 平均解 | 方差 | |
C101 | 418.42 | 418.42 | 418.42 | 0.00 | 418.42 | 419.19 | 418.50 | 0.16 | 418.42 | 420.28 | 419.99 | 0.62 |
C102 | 418.11 | 430.02 | 421.99 | 4.78 | 417.34 | 431.41 | 420.58 | 5.01 | 417.34 | 430.83 | 424.04 | 4.92 |
C103 | 416.88 | 432.63 | 420.46 | 5.57 | 416.06 | 442.31 | 424.93 | 9.82 | 417.49 | 456.05 | 427.91 | 13.43 |
C104 | 360.51 | 427.72 | 390.46 | 26.57 | 360.83 | 461.17 | 408.86 | 27.25 | 396.12 | 420.97 | 411.36 | 8.05 |
C201 | 373.55 | 388.14 | 379.90 | 6.77 | 373.55 | 388.14 | 376.92 | 5.73 | 373.55 | 378.99 | 375.97 | 1.62 |
C202 | 388.52 | 441.26 | 418.05 | 24.35 | 366.78 | 388.52 | 372.64 | 8.18 | 366.78 | 420.33 | 397.78 | 22.89 |
C203 | 366.82 | 374.18 | 370.93 | 2.98 | 371.81 | 376.90 | 372.56 | 1.53 | 366.82 | 407.89 | 378.60 | 13.95 |
C204 | 365.86 | 411.77 | 379.21 | 12.64 | 365.86 | 401.50 | 375.24 | 10.49 | 369.02 | 383.83 | 373.20 | 3.66 |
R101 | 1048.04 | 1057.54 | 1052.98 | 3.08 | 1046.70 | 1066.76 | 1053.24 | 5.32 | 1047.84 | 1056.97 | 1052.94 | 2.78 |
R102 | 912.24 | 924.37 | 916.17 | 3.82 | 911.44 | 997.17 | 923.96 | 25.57 | 911.44 | 934.77 | 917.98 | 5.34 |
R103 | 783.45 | 798.88 | 786.35 | 4.36 | 775.65 | 820.08 | 784.89 | 12.41 | 775.65 | 806.53 | 789.03 | 10.49 |
R104 | 651.45 | 657.72 | 653.48 | 2.01 | 642.13 | 661.44 | 647.68 | 7.66 | 635.96 | 660.73 | 651.34 | 8.54 |
R201 | 802.07 | 845.03 | 816.50 | 10.88 | 808.53 | 854.37 | 823.74 | 12.92 | 803.04 | 845.10 | 824.93 | 11.36 |
R202 | 714.19 | 772.25 | 735.30 | 14.52 | 714.19 | 771.23 | 736.59 | 18.50 | 714.19 | 756.67 | 737.10 | 12.13 |
R203 | 615.08 | 673.72 | 647.06 | 21.18 | 620.59 | 675.02 | 639.52 | 16.54 | 614.82 | 722.89 | 663.89 | 30.63 |
R204 | 511.40 | 546.25 | 519.35 | 12.91 | 515.12 | 544.80 | 527.90 | 10.69 | 514.28 | 526.28 | 518.62 | 3.22 |
RC101 | 968.80 | 982.97 | 976.81 | 3.44 | 958.59 | 973.79 | 965.57 | 6.03 | 967.88 | 984.74 | 975.38 | 4.53 |
RC102 | 887.07 | 904.79 | 894.27 | 4.84 | 886.47 | 901.82 | 891.44 | 4.66 | 886.47 | 902.18 | 894.11 | 4.77 |
RC103 | 833.68 | 844.12 | 836.85 | 3.74 | 823.98 | 972.06 | 846.46 | 42.64 | 819.39 | 882.93 | 847.35 | 17.23 |
RC104 | 646.09 | 688.60 | 675.40 | 10.78 | 639.28 | 719.64 | 672.29 | 21.04 | 636.99 | 679.35 | 655.40 | 14.36 |
RC201 | 686.31 | 764.68 | 725.55 | 39.00 | 686.31 | 756.72 | 693.35 | 21.00 | 686.31 | 755.57 | 709.90 | 19.46 |
RC202 | 684.20 | 781.68 | 708.43 | 28.90 | 615.04 | 725.06 | 643.61 | 35.44 | 615.04 | 722.08 | 662.97 | 28.25 |
RC203 | 596.01 | 696.43 | 650.48 | 43.59 | 559.68 | 675.21 | 600.77 | 33.79 | 559.21 | 693.16 | 657.27 | 40.19 |
RC204 | 516.81 | 523.66 | 521.38 | 2.22 | 471.82 | 521.21 | 481.36 | 19.18 | 459.77 | 523.52 | 497.30 | 22.89 |
Avg | 623.57 | 657.78 | 638.16 | 12.21 | 615.26 | 664.40 | 629.28 | 15.07 | 615.58 | 657.19 | 636.01 | 12.72 |
表3
算例对比结果"
算例 | n | VNS | GA-VNS | 本文算法 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|
C1 | 20 | 4 | 1588.27 | 4 | 1607.88 | 4 | 1555.82 | 0 | 0 | 2.09% | 3.35% |
C2 | 40 | 8.5 | 3498.66 | 8.6 | 3394.78 | 8 | 3284.92 | 0.5 | 0.6 | 6.51% | 3.34% |
C3 | 60 | 12.2 | 5387.93 | 12.5 | 5282.61 | 11.3 | 4826.71 | 0.9 | 1.2 | 11.63% | 9.45% |
C4 | 80 | 15.6 | 8058.39 | 16 | 7549.56 | 15.2 | 6778.09 | 0.4 | 0.8 | 18.89% | 11.38% |
C5 | 100 | 19.5 | 9986.01 | 20 | 10067.23 | 19 | 8859.76 | 0.5 | 1 | 12.71% | 13.63% |
R1 | 20 | 6 | 2170.02 | 6 | 2121.22 | 5.2 | 2102.86 | 0.8 | 0.8 | 3.19% | 0.87% |
R2 | 40 | 12.1 | 4783.28 | 11 | 4735.83 | 11 | 4463.65 | 1.1 | 0 | 7.16% | 6.10% |
R3 | 60 | 17.6 | 7243.21 | 16.8 | 6931.83 | 15.7 | 6426.65 | 1.9 | 1.1 | 12.71% | 7.86% |
R4 | 80 | 24.4 | 10194.92 | 23.2 | 9815.30 | 21.5 | 8828.04 | 2.9 | 1.7 | 15.48% | 11.18% |
R5 | 100 | 30 | 11930.52 | 28.6 | 11824.46 | 26.1 | 10855.80 | 3.9 | 2.5 | 9.90% | 8.92% |
RC1 | 20 | 6 | 2188.95 | 5.8 | 2154.51 | 5 | 2054.95 | 1 | 0.8 | 6.52% | 4.85% |
RC2 | 40 | 11.7 | 4947.02 | 11 | 4863.90 | 11 | 4563.89 | 0.7 | 0 | 8.39% | 6.57% |
RC3 | 60 | 18 | 7547.59 | 17.7 | 7280.69 | 15.9 | 6756.87 | 2.1 | 1.8 | 11.70% | 7.75% |
RC4 | 80 | 23.6 | 10146.03 | 22.9 | 10038.30 | 21.5 | 8999.30 | 2.1 | 1.4 | 12.74% | 11.55% |
RC5 | 100 | 30 | 13512.58 | 29.4 | 12846.92 | 26.7 | 11028.82 | 3.3 | 2.7 | 22.52% | 16.48% |
Avg | 15.95 | 6878.89 | 15.57 | 6701.00 | 14.47 | 6092.41 | 1.47 | 1.09 | 12.91% | 9.99% |
表4
固定碳配额下不同碳交易价格试验结果表"
碳价格 (元/kg) | 碳排放量 (kg) | 碳成本 (元) | 总成本 (元) | 比例 |
---|---|---|---|---|
0 | 466.41 | 0 | 10257.83 | 0.00% |
0.05 | 466.02 | 18.30 | 10272.31 | 0.18% |
0.15 | 466.38 | 54.96 | 10309.14 | 0.53% |
0.25 | 464.56 | 91.14 | 10320.28 | 0.88% |
0.5 | 450.37 | 175.18 | 10855.80 | 1.61% |
1 | 431.70 | 331.70 | 10914.05 | 3.03% |
1.5 | 429.50 | 494.26 | 11090.54 | 4.46% |
2 | 428.84 | 657.68 | 11168.74 | 5.89% |
2.5 | 426.20 | 815.50 | 11349.45 | 7.19% |
3 | 426.00 | 978.00 | 12082.90 | 8.09% |
5 | 423.94 | 1619.68 | 12964.31 | 12.49% |
7.5 | 423.52 | 2426.40 | 13880.08 | 17.48% |
10 | 423.26 | 3232.64 | 14884.29 | 21.72% |
表5
不同碳交易价格、碳配额实验结果"
碳交易价格 (元/kg) | 碳配额 (Kg) | 碳排放量 (Kg) | 成本 (元) | 总成本 (元) |
---|---|---|---|---|
0.5 | 0 | 450.37 | 225.19 | 10930.80 |
50 | 450.37 | 200.19 | 10905.80 | |
100 | 450.37 | 175.19 | 10880.80 | |
150 | 450.37 | 150.19 | 10855.80 | |
200 | 450.37 | 125.19 | 10830.80 | |
250 | 450.37 | 100.19 | 10805.80 | |
300 | 450.37 | 75.19 | 10780.80 | |
0.75 | 0 | 439.11 | 428.07 | 10966.36 |
50 | 439.11 | 390.57 | 10928.86 | |
100 | 439.11 | 353.07 | 10891.36 | |
150 | 439.11 | 315.57 | 10853.86 | |
200 | 439.11 | 278.07 | 10816.36 | |
250 | 439.11 | 240.57 | 10778.86 | |
300 | 439.11 | 203.07 | 10741.36 | |
1 | 0 | 431.70 | 543.38 | 11014.05 |
50 | 431.70 | 493.38 | 10964.05 | |
100 | 431.70 | 443.38 | 10914.05 | |
150 | 431.70 | 393.38 | 10864.05 | |
200 | 431.70 | 343.38 | 10814.05 | |
250 | 431.70 | 293.38 | 10764.05 | |
300 | 431.70 | 243.38 | 10714.05 |
表6
配送结果对比"
算例 | 数目 | 多车厢 | 单车厢 | |||||||
---|---|---|---|---|---|---|---|---|---|---|
C1 | 20 | 4 | 1555.82 | 76.19% | 4 | 1737.22 | 76.19% | 0 | 11.66% | 0 |
C2 | 40 | 8 | 3284.92 | 78.31% | 9 | 3714.25 | 69.61% | 1 | 13.07% | 8.70% |
C3 | 60 | 11.3 | 4826.71 | 83.16% | 13 | 5534.78 | 72.29% | 1.7 | 14.67% | 10.88% |
C4 | 80 | 15.2 | 6778.09 | 80.76% | 18.2 | 7978.49 | 67.45% | 3 | 17.71% | 13.31% |
C5 | 100 | 19 | 8859.76 | 81.99% | 23.3 | 10467.81 | 66.86% | 4.3 | 18.15% | 15.13% |
R1 | 20 | 5.2 | 2102.86 | 78.21% | 5.7 | 2236.60 | 71.35% | 0.5 | 6.36% | 6.86% |
R2 | 40 | 11 | 4463.65 | 77.78% | 12.3 | 4996.61 | 69.56% | 1.3 | 11.94% | 8.22% |
R3 | 60 | 15.7 | 6426.65 | 81.05% | 16.6 | 6979.98 | 76.65% | 0.9 | 8.61% | 4.39% |
R4 | 80 | 21.5 | 8828.04 | 80.30% | 23 | 9697.60 | 75.06% | 1.5 | 9.85% | 5.24% |
R5 | 100 | 26.1 | 10855.80 | 82.56% | 28.7 | 12344.13 | 75.08% | 2.6 | 13.71% | 7.48% |
RC1 | 20 | 5 | 2054.95 | 81.34% | 5.5 | 2284.07 | 73.94% | 0.5 | 11.15% | 7.39% |
RC2 | 40 | 11 | 4563.89 | 77.78% | 12.7 | 5148.07 | 67.36% | 1.7 | 12.80% | 10.41% |
RC3 | 60 | 15.9 | 6756.87 | 80.03% | 17 | 7373.77 | 74.85% | 1.1 | 9.13% | 5.18% |
RC4 | 80 | 21.5 | 8999.30 | 80.30% | 24.5 | 10140.41 | 70.46% | 3 | 12.68% | 9.83% |
RC5 | 100 | 26.7 | 11028.82 | 80.70% | 31.6 | 12576.16 | 68.19% | 4.9 | 14.03% | 12.51% |
Avg | 14.47 | 6092.41 | 80.03% | 16.34 | 6880.67 | 71.66% | 1.87 | 12.94% | 8.37% |
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