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Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences

  • * Corresponding author: Dr Rongjuan Luo

    * Corresponding author: Dr Rongjuan Luo

This research was supported by National Science Foundation of China [grant numbers 71572031, 71971049 and 71702112]

Abstract Full Text(HTML) Figure(7) / Table(8) Related Papers Cited by
  • A combined location-routing-inventory system (CLRIS) in a three-echelon supply chain network is studied with environmental considerations. Specifically, a bi-objective mixed integer programming model is formulated for the CLRIS to deal with the trade-offs between the total cost and the carbon-capped difference (CCD). A multi-objective particle swarm optimization (MOPSO) heuristic solution procedure is developed and implemented to solve the bi-objective mixed integer programming problem. The bi-objective mixed integer programming model and the MOPSO heuristic procedure are applied to a real-life problem as an illustrative example. The approximate nondominated frontier formed by solutions not dominated by others can be used for the decision makers to make trade-offs between the total cost and the CCD. Sensitivity analyses are conducted, and the relationship among the carbon cap, CCD, the total cost and the carbon prices are examined, and relevant managerial insights are provided. Comparisons with other existing algorithms show that the MSPSO heuristic procedure has very good performance.

    Mathematics Subject Classification: Primary: 65K05; Secondary: 90C08.

    Citation:

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  • Figure 1.  A three-echelon supply chain network

    Figure 2.  Locations of the Plants, the potential DCs and the Retailers

    Figure 3.  The nondominated frontier of the CLRIS considering CCD

    Figure 4.  The nondominated frontier of the CLRIS considering carbon emissions

    Figure 5.  Nondominated frontiers of the model minimizing CCD by varying the carbon cap

    Figure 6.  Box plots for the three evaluation indicators

    Figure 7.  The obtained nondominated frontiers of the all three procedures

    Table 1.  Summary of relevant literature for low carbon supply chains

    Literature category Issues considered Related publications
    Translating carbon emissions into cost Carbon cost; carbon price; pollution cost; cap-and-trade; emissions trading scheme Tseng and Hung [44]; Treitl et al. [43]; Alhaj et al. [1]; Bai et al. [5]; Wang, Tao and Shi [50].
    Treating carbon emissions as a constraint in supply chain models Carbon footprints; carbon-constrained Benjaafar et al. [8]; Xu et al. [53]; Lam and Gu [23]; Martí et al. [26].
    Policies for carbon emission reduction Carbon trading; carbon tax Bazan et al. [7]; Wang et al. [47]; Wang, Zhao and Herty [49]; Saxena et al. [34]; Xin et al. [51]; Huang et al. [18]; Samuel et al. [33].
    Multiple objectives with carbon emissions Trade-offs between cost and environment Paksoy et al. [30]; Musavi and Bozorgi-Amiri [29]; Daryanto et al. [10].
    Carbon emission reduction with coordination mechanisms Green production; green purchasing; coordination mechanism; life cycle assessment Palmer [31]; Jaber et al. [19]; Du et al. [13]; Xu et al. [52]; Zhang et al. [56].
    Supply chain network design Location; routing; inventory Min et al. [27]; Wang, Tao and Shi [50]; Javid and Azad [20]; Farahani et al. [15]; Tang et al. [42]; Zhalechian et al. [55].
     | Show Table
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    Table 2.  Distances from the plants to the potential DCs (km)

    Shenbei Yuhong Sujiatun Dongling
    Fushun 77.5 71.1 64.6 36.5
    Liaoyang 112.8 65.5 44.7 35.8
     | Show Table
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    Table 3.  Parameters of the potential DCs

    Shenbei Yuhong Sujiatun Dongling
    Lead time (days) 3 2 3 4
    Service level 95% 95% 95% 95%
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    Table 4.  Areas and fixed costs of the potential DCs

    Capacity (ton) Fixed cost per period () Holding cost (/ton/day) Areas (m2)
    Shenbei 340 20000 0.20 1100
    Yuhong 500 18000 0.25 1600
    Sujiatun 310 11200 0.20 1000
    Dongling 380 15600 0.25 1200
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    Table 5.  Details of some typical solutions on the nondominated frontier

    Solutions Plants DC Status Total cost CCD
    Shenbei Yuhong Sujiatun Dongling
    1 Fushun 1 0 1 1 80153.5 4451.7
    Liaoyang 1 0 0 0
    2 Fushun 1 1 0 1 81875.5 3677.2
    Liaoyang 1 1 0 0
    3 Fushun 0 1 0 1 88125.9 3025.7
    Liaoyang 1 1 0 0
    4 Fushun 1 1 0 1 93750.3 2418.4
    Liaoyang 1 1 0 1
    5 Fushun 1 1 0 1 100104.9 1975.1
    Liaoyang 1 1 1 0
    6 Fushun 1 1 1 0 110139.3 1575.7
    Liaoyang 1 0 1 0
    7 Fushun 1 1 1 0 117697.4 1273.5
    Liaoyang 1 1 1 0
    8 Fushun 0 1 1 1 122385.8 968.1
    Liaoyang 0 1 1 1
    9 Fushun 1 1 1 1 134982.2 613.9
    Liaoyang 0 1 1 1
     | Show Table
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    Table 6.  Values of the evaluation indicators for MOPSO, NSGAII and MOEA/D

    Convergence Diversity Dominance
    MOPSO NSGAII MOEA/D MOPSO NSGAII MOEA/D MOPSO NSGAII MOEA/D
    1 0.258 0.179 2.320 0.507 0.518 0.691 0.909 0.476 0.000
    2 0.126 0.251 2.261 0.520 0.494 0.775 0.878 0.466 0.000
    3 0.193 0.142 1.208 0.508 0.540 0.694 0.814 0.485 0.000
    4 0.170 0.254 1.273 0.516 0.482 0.841 0.828 0.441 0.000
    5 0.160 0.244 1.679 0.468 0.471 0.738 0.913 0.428 0.000
    6 0.158 0.260 1.741 0.559 0.479 0.808 0.820 0.463 0.000
    7 0.137 0.241 1.375 0.493 0.497 0.698 0.826 0.535 0.000
    8 0.177 0.106 2.207 0.480 0.627 0.817 0.775 0.517 0.000
    9 0.233 0.092 1.471 0.516 0.545 0.728 0.789 0.371 0.000
    10 0.250 0.103 1.050 0.455 0.493 0.713 0.834 0.526 0.000
    11 0.239 0.171 1.607 0.521 0.598 0.789 0.817 0.330 0.000
    12 0.106 0.179 1.800 0.485 0.557 0.804 0.892 0.326 0.000
    13 0.146 0.188 1.952 0.406 0.533 0.724 0.884 0.478 0.000
    14 0.131 0.181 1.667 0.490 0.493 0.704 0.871 0.448 0.000
    15 0.115 0.158 2.385 0.433 0.449 0.779 0.905 0.476 0.000
    16 0.158 0.195 2.158 0.530 0.482 0.662 0.868 0.557 0.000
    17 0.122 0.268 1.276 0.480 0.485 0.710 0.841 0.486 0.000
    18 0.193 0.169 1.727 0.489 0.517 0.663 0.892 0.546 0.000
    19 0.168 0.220 1.700 0.550 0.576 0.637 0.926 0.403 0.000
    20 0.172 1.295 1.333 0.478 0.567 0.787 0.833 0.353 0.000
    21 0.143 1.724 1.696 0.502 0.517 0.708 0.866 0.303 0.000
     | Show Table
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    Table A1.  Distances from the potential DCs to the retailers (km)

    Shenbei Yuhong Dongling
    1 82.6 47.7 55.6
    2 80.1 47.0 37.3
    3 80.5 27.9 54.2
    4 64.5 35.7 42.3
    5 62.3 40.0 47.3
    6 64.6 49.8 15.7
    7 61.2 55.6 7.0
    8 58.2 45.0 27.3
    9 64.2 36.1 49.1
    10 66.1 27.2 49.5
    11 66.0 12.0 50.0
    12 66.2 48.2 60.1
    13 63.8 60.6 12.0
    14 56.6 40.2 58.9
    15 55.2 35.2 67.1
    16 58.1 7.0 55.3
    17 62.1 54.2 42.0
    18 56.9 42.1 41.1
    19 50.3 38.4 47.9
    20 45.7 39.0 52.1
    21 50.1 32.2 50.0
    22 50.1 12.0 57.1
    23 40.1 36.1 37.0
    24 50.1 48.9 12.2
    25 30.2 45.9 52.1
    26 25.8 40.1 67.1
    27 32.1 40.2 55.3
    28 23.2 38.4 55.3
    29 25.8 42.6 65.1
    30 22.4 48.9 54.2
    31 20.5 52.6 62.1
    32 23.7 46.0 70.1
    33 7.0 55.6 66.2
    34 15.0 61.3 72.1
     | Show Table
    DownLoad: CSV

    Table A2.  Distances between the retailers (km)

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
    1 0.0 17.1 15.9 18.7 50.2 52.5 55.6 52.5 48.9 50.2 49.5 48.9 58.8 52.5 47.9 51.1 60.0 50.1 52.5 49.1 50.2 50.2 55.3 55.3 56.3 52.1 56.3 62.3 67.3 69.2 70.1 75.2 77.1
    2 17.1 0.0 18.7 7.0 10.1 18.8 50.2 20.1 15.9 15.9 24.1 52.5 55.1 18.8 19.8 45.1 53.2 47.1 20.1 50.2 50.2 51.2 53.2 54.7 55.7 53.2 54.9 66.1 66.1 67.1 67.1 69.2 70.1
    3 15.9 18.7 0.0 17.3 47.5 49.9 52.1 48.5 45.2 17.3 16.6 16.8 60.0 45.2 47.5 45.7 60.0 49.9 45.1 46.2 44.1 50.3 60.3 60.0 57.3 49.8 55.1 57.3 57.3 60.1 61.3 67.1 68.9
    4 18.7 7.0 17.3 0.0 7.0 55.1 40.1 30.2 25.1 7.0 15.2 32.1 41.9 30.2 27.1 25.7 41.9 56.2 30.2 29.5 35.1 26.7 36.9 36.3 41.9 39.1 36.9 50.1 53.4 57.3 59.9 64.7 66.3
    5 50.2 10.1 47.5 7.0 0.0 7.0 49.6 7.2 5.9 28.1 50.5 25.8 32.6 27.1 13.8 45.1 32.6 44.3 40.1 46.2 49.9 43.2 32.6 36.6 39.8 39.8 37.6 55.3 55.3 59.9 62.0 65.0 66.0
    6 52.5 18.8 49.9 55.1 7.0 0.0 18.8 8.7 20.4 24.1 29.4 48.9 55.1 55.1 57.8 35.9 54.1 55.1 54.1 32.4 48.9 58.8 57.8 48.9 53.9 54.8 55.5 58.4 58.7 62.4 67.1 68.6 68.1
    7 55.6 50.2 52.1 40.1 49.6 18.8 0.0 18.8 49.6 50.2 47.1 52.1 5.1 49.6 50.2 54.1 10.0 49.8 47.1 50.1 52.1 48.6 19.8 19.6 23.8 50.1 50.2 49.2 46.3 54.1 59.2 59.2 60.1
    8 52.5 20.1 48.5 30.2 7.2 8.7 18.8 0.0 6.4 15.6 20.6 28.7 19.6 14.2 20.6 35.9 19.6 24.2 22.1 20.6 28.7 19.6 20.6 28.7 30.7 32.5 34.6 50.3 45.3 50.3 54.2 55.2 66.4
    9 48.9 15.9 45.2 25.1 5.9 20.4 49.6 6.4 0.0 15.2 18.9 25.8 26.8 6.4 15.2 35.6 26.8 27.8 10.1 35.6 38.9 30.2 38.9 39.7 40.1 37.8 41.1 45.6 45.8 47.6 50.2 50.6 50.9
    10 50.2 15.9 17.3 7.0 28.1 24.1 50.2 15.6 15.2 0.0 5.0 17.3 55.1 15.2 5.0 15.9 45.2 36.8 15.2 36.8 38.8 39.6 45.2 43.2 43.2 40.1 43.2 45.4 47.9 47.4 45.2 52.1 52.0
    11 50.2 24.1 16.6 15.2 50.5 29.4 47.1 20.6 18.9 5.0 0.0 10.0 45.9 27.1 9.0 7.1 27.1 20.1 16.9 16.9 17.5 18.9 27.1 26.7 27.1 25.9 32.2 36.5 45.9 47.2 46.2 53.1 53.0
    12 48.9 52.5 16.8 32.1 25.8 48.9 52.1 28.7 25.8 17.3 10.0 0.0 60.0 25.8 9.2 10.0 50.0 40.3 25.8 11.2 12.3 40.3 49.0 45.1 44.3 40.3 44.5 40.3 50.1 53.7 56.5 58.2 59.9
    13 58.8 55.1 60.0 41.9 32.6 55.1 5.1 19.6 26.8 55.1 45.9 60.0 0.0 35.6 41.9 45.9 12.1 20.3 32.6 50.1 45.9 35.6 17.0 43.1 45.1 55.1 58.1 59.8 45.1 62.8 69.1 59.8 60.2
    14 52.5 18.8 45.2 30.2 27.1 55.1 49.6 14.2 6.4 15.2 27.1 25.8 35.6 0.0 6.2 15.2 45.1 16.1 5.9 23.3 29.1 20.1 40.1 38.7 38.5 29.1 32.1 37.7 39.8 42.3 45.2 46.6 47.9
    15 47.9 19.8 47.5 27.1 13.8 57.8 50.2 20.6 15.2 5.0 9.0 9.2 41.9 6.2 0.0 15.2 45.7 48.9 10.2 15.6 20.1 21.2 40.7 41.2 40.2 38.0 40.2 43.5 45.1 47.9 47.1 48.2 48.9
    16 51.1 45.1 45.7 25.7 45.1 35.9 54.1 35.9 35.6 15.9 7.1 10.0 45.9 15.2 15.2 0.0 37.1 29.1 25.7 10.1 11.1 23.4 37.1 32.7 33.3 23.4 30.0 31.2 36.1 46.1 45.2 47.7 49.2
    17 60.0 53.2 60.0 41.9 32.6 54.1 10.0 19.6 26.8 45.2 27.1 50.0 12.1 45.1 45.7 37.1 0.0 18.7 21.1 45.2 44.5 25.6 8.8 18.7 25.5 45.2 46.6 55.8 45.1 50.1 68.1 63.1 60.0
    18 52.1 50.2 45.2 39.1 49.8 18.8 10.0 22.1 25.9 40.1 23.1 48.9 15.0 25.9 57.8 31.2 11.9 7.7 18.8 40.1 44.4 21.8 7.5 44.4 24.5 43.1 46.8 48.7 40.1 45.1 55.1 58.1 58.7
    19 50.1 47.1 49.9 56.2 44.3 55.1 49.8 24.2 27.8 36.8 20.1 40.3 20.3 16.1 48.9 29.1 18.7 0.0 7.4 35.9 40.6 10.0 22.7 20.0 24.7 27.8 35.7 40.7 49.7 50.7 52.3 57.9 58.7
    20 52.5 20.1 45.1 30.2 40.1 54.1 47.1 22.1 10.1 15.2 16.9 25.8 32.6 5.9 10.2 25.7 21.1 7.4 0.0 20.1 25.5 5.6 27.6 28.7 32.5 30.7 35.7 45.1 45.0 43.1 48.7 49.2 50.1
    21 49.1 50.2 46.2 29.5 46.2 32.4 50.1 20.6 35.6 36.8 16.9 11.2 50.1 23.3 15.6 10.1 45.2 35.9 20.1 0.0 8.5 22.2 40.7 34.5 32.1 18.7 24.5 38.0 42.7 43.0 43.7 45.6 46.5
    22 50.2 50.2 44.1 35.1 49.9 48.9 52.1 28.7 38.9 38.8 17.5 12.3 45.9 29.1 20.1 11.1 44.5 40.6 25.5 8.5 0.0 27.8 45.2 40.1 38.1 18.9 26.0 30.1 44.1 44.6 45.0 46.7 48.0
    23 50.2 51.2 50.3 26.7 43.2 58.8 48.6 19.6 30.2 39.6 18.9 40.3 35.6 20.1 21.2 23.4 25.6 10.0 5.6 22.2 27.8 0.0 27.1 14.2 15.8 20.7 24.2 33.3 38.9 40.1 43.3 45.1 45.2
    24 55.3 53.2 60.3 36.9 32.6 57.8 19.8 20.6 38.9 45.2 27.1 49.0 17.0 40.1 40.7 37.1 8.8 22.7 27.6 40.7 45.2 27.1 0.0 13.6 19.5 33.2 34.8 45.2 33.8 38.5 46.1 55.1 50.1
    25 55.3 54.7 60.0 36.3 36.6 48.9 19.6 28.7 39.7 43.2 26.7 45.1 43.1 38.7 41.2 32.7 18.7 20.0 28.7 34.5 40.1 14.2 13.6 0.0 6.1 18.9 17.0 41.8 20.0 25.0 40.0 45.2 46.1
    26 56.3 55.7 57.3 41.9 39.8 53.9 23.8 30.7 40.1 43.2 27.1 44.3 45.1 38.5 40.2 33.3 25.5 24.7 32.5 32.1 38.1 15.8 19.5 6.1 0.0 20.0 17.9 36.1 30.1 36.1 36.2 37.1 38.2
    27 52.1 53.2 49.8 39.1 39.8 54.8 50.1 32.5 37.8 40.1 25.9 40.3 55.1 29.1 38.0 23.4 45.2 27.8 30.7 18.7 18.9 20.7 33.2 18.9 20.0 0.0 7.3 18.2 36.2 38.1 38.1 40.2 44.2
    28 56.3 54.9 55.1 36.9 37.6 55.5 50.2 34.6 41.1 43.2 32.2 44.5 58.1 32.1 40.2 30.0 46.6 35.7 35.7 24.5 26.0 24.2 34.8 17.0 17.9 7.3 0.0 13.5 30.1 36.9 40.2 42.1 43.5
    29 62.3 66.1 57.3 50.1 55.3 58.4 49.2 50.3 45.6 45.4 36.5 40.3 59.8 37.7 43.5 31.2 55.8 40.7 45.1 38.0 30.1 33.3 45.2 41.8 36.1 18.2 13.5 0.0 35.6 37.3 20.0 45.2 46.2
    30 67.3 66.1 57.3 53.4 55.3 58.7 46.3 45.3 45.8 47.9 45.9 50.1 45.1 39.8 45.1 36.1 45.1 49.7 45.0 42.7 44.1 38.9 33.8 20.0 30.1 36.2 30.1 35.6 0.0 7.2 37.3 30.2 32.1
    31 69.2 67.1 60.1 57.3 59.9 62.4 54.1 50.3 47.6 47.4 47.2 53.7 62.8 42.3 47.9 46.1 50.1 50.7 43.1 43.0 44.6 40.1 38.5 25.0 36.1 38.1 36.9 37.3 7.2 0.0 25.6 20.1 26.1
    32 70.1 67.1 61.3 59.9 62.0 67.1 59.2 54.2 50.2 45.2 46.2 56.5 69.1 45.2 47.1 45.2 68.1 52.3 48.7 43.7 45.0 43.3 46.1 40.0 36.2 38.1 40.2 20.0 37.3 25.6 0.0 38.2 45.6
    33 75.2 69.2 67.1 64.7 65.0 68.6 59.2 55.2 50.6 52.1 53.1 58.2 59.8 46.6 48.2 47.7 63.1 57.9 49.2 45.6 46.7 45.1 55.1 45.2 37.1 40.2 42.1 45.2 30.2 20.1 38.2 0.0 8.2
    34 77.1 70.1 68.9 66.3 66.0 68.1 60.1 66.4 50.9 52.0 53.0 59.9 60.2 47.9 48.9 49.2 60.0 58.7 50.1 46.5 48.0 45.2 50.1 46.1 38.2 44.2 43.5 46.2 32.1 26.1 45.6 8.2 0.0
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