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A multi-objective decision-making model for supplier selection considering transport discounts and supplier capacity constraints

  • * Corresponding author: Alireza Eydi

    * Corresponding author: Alireza Eydi 
Abstract Full Text(HTML) Figure(7) / Table(7) Related Papers Cited by
  • The present study considers the transport discounts and capacity constraints for the suppliers and manufacturers simultaneously to provide a multi-objective decision-making model for supplier selection on a three-level supply chain. For this purpose, it begins with presenting a nonlinear mixed-integer model of the problem, where the objectives include the minimization of the logistics costs and lead time. Subsequently, the NSGA-Ⅱ algorithm is developed to solve the large-scale model of the problem and simultaneously optimize the two objectives to achieve Pareto-optimal solutions. To test the efficiency of the proposed algorithm, several synthetic examples of various sizes are then generated and solved. Finally, the paper compares the performance of the proposed metaheuristic algorithm with the augmented epsilon-constraint method. In summary, the findings of this study provided researchers and industries to easily access to a cohesive model of supplier selection considering transportation that are essential to the solution of many real-world challenging logistics issues.

    Mathematics Subject Classification: Primary: 90B06.

    Citation:

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  • Figure 1.  Demonstration of a chromosome (i.e., a solution) in the proposed metaheuristic algorithm

    Figure 2.  Demonstration of the solution of the case study

    Figure 4.  Demonstration of the mutation operator

    Figure 4.  Demonstration of the mutation operator

    Figure 5.  Setting the parameters of the algorithm

    Figure 6.  Comparison of the Pareto front for a numerical example

    Figure 7.  The Pareto front for a large-scale example

    Table 1.  Details of the sample problems

    Sample No. No. of suppliers No. of warehouses No. of customers No. of price levels
    1 2 2 3 2
    2 2 2 4 2
    3 2 3 5 2
    4 3 3 4 2
    5 3 4 6 2
    6 3 5 8 2
    7 4 4 8 2
    8 4 6 12 2
    9 4 8 16 2
    10 20 30 40 2
    11 25 20 45 2
    12 30 25 50 2
    13 2 2 4 4
    14 2 3 5 4
    15 3 3 4 4
    16 3 4 6 4
     | Show Table
    DownLoad: CSV

    Table 2.  Parametrization of the algorithm

    The initial population 40-30-20 Mutation rate 0.1-0.3-0.5
    Maximum No. of iterations 400-300-100 Crossover rate 0.9-0.7-0.5
     | Show Table
    DownLoad: CSV

    Table 3.  Results of the parametrization of the proposed metaheuristic algorithm

    The initial population 30 Penalty for violation of storage capacity 30000
    Maximum No. of iterations 300 Penalty for violation of supplier capacity 30000
    Crossover rate 0.7 Penalty for violation of type Ⅰ carrier capacity 30000
    Mutation rate 0.3 Penalty for violation of type Ⅱ carrier capacity 30000
     | Show Table
    DownLoad: CSV

    Table 4.  Sample problems with two price levels

    Example number Solutions of the mathematical model Metaheuristic algorithm The number of Pareto solutions Solution time(s)
    Total cost Lead time Total cost Lead time Mathematical model Metaheuristic algorithm Mathematical model Metaheuristic algorithm
    1 68341.34 192.79 68341.34 192.79 5 23 5 21
    38878.15 240.99 38878.15 240.99
    2 121651.55 314.90 11737.38 314.90 5 24 8 24
    64614.87 574.81 64614.87 574.81
    3 75789.91 235.26 78716.08 235.23 6 27 782 21
    53963.32 318.05 52274.41 327.23
    4 78533.08 209.05 78716.08 209.07 8 27 70 21
    43011.82 303.94 42183.37 431.03
    5 81293.42 291.36 87200.36 270.90 9 38 2713 22
    50979.63 531.78 49854.45 645.99
    6 219299.25 556.65 221539.56 591.10 5 38 2471 18
    137964.35 1043.08 136235.26 991.28
    7 150034.73 456.26 145148.71 454.95 2 28 1221 17
    121703.96 696.96 104719.58 738.18
    8 - - 197548.38 454.95 0 59 3600 17
    - - 141281.50 1336.12
    9 - - 317966.30 1410.04 0 63 7200 9
    - - 295530.83 1898.55
    10 - - 692358.54 3516.57 - 538 - 15
    - - 614931.40 5127.21
    11 - - 1395014.66 304484.07 - 436 - 9
    - - 1358331.99 305700.94
    12 - - 1319417.25 274612.41 - 693 - 9
    - - - -
     | Show Table
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    Table 5.  Sample problems with four price levels

    Example number Mathematical model solutions Metaheuristic algorithm The number of Pareto solutions Solution time(s)
    Total cost Lead time Total cost Lead time Mathematical model Metaheuristic algorithm Mathematical model Metaheuristic algorithm
    13 58818.69 178.97 55591.93 178.97 12 37 12 16
    53372.19 192.41 48951.15 438.95
    14 85499.87 351.63 92925.05 92925.05 2090 40 5 23
    62789.30 492.64 62935.46 497.88
    15 83856.96 263.83 99922.57 253.48 2113 33 9 22
    53647.19 605.75 53384.45 593.19
    16 108712.51 369.94 100694.07 394.24 2373 42 6 14
           
     | Show Table
    DownLoad: CSV

    Table 6.  Comparison of the proposed mathematical model and algorithm based on diversity and spread criteria

    Example No. Spread criterion Diversity and uniformity criteria
    Mathematical model Metaheuristic algorithm Mathematical model Metaheuristic algorithm
    1 29714.36 29463.23 0.97 1.43
    2 54007.81 52753.16 0.60 1.68
    3 19401.56 26441.83 0.65 0.85
    4 14492.95 25051.45 0.52 1.00
    5 25165.95 37347.79 0.24 0.78
    6 41666.65 85305.24 0.74 1.10
    7 28331.79 40430.12 - 1.00
    8 - 29245.55 - 0.93
    9 - 22440.79 - 0.74
    10 - 77443.89 - 0.92
    11 - 36702.85 - 0.80
    12 - 220125.97 - 1.51
    13 5446.50 6645.87 0.68 0.99
    14 11106.65 2990.05 0.32 0.77
    15 28204.12 46539.36 0.24 0.97
    16 9979.74 15707.09 0.72 0.93
     | Show Table
    DownLoad: CSV

    Table 7.  Comparison between different solution methods regarding average processing time and the number of Pareto solutions obtained for the small-sized problem

    Methodology Average processing time (in seconds) The number of Pareto solutions
    augmented epsilon-constraint method 1897 6
    Metaheuristic algorithm 38 19
     | Show Table
    DownLoad: CSV
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