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A multi-objective integrated model for closed-loop supply chain configuration and supplier selection considering uncertain demand and different performance levels

  • * Corresponding author: Masoud Mohammadzadeh

    * Corresponding author: Masoud Mohammadzadeh 
Abstract / Introduction Full Text(HTML) Figure(4) / Table(5) Related Papers Cited by
  • In the supply chain management, configuration of supply chain is the most important decision in the long term and supplier selection and order allocation are the most important decision in the medium-term that are considered separately. Considering these together can overcome the sub-optimality. This paper deals with an integrated model that has two phases. In the first phase, we present a framework for supplier selection criteria in Closed Loop Supply Chain (CLSC). In addition, we define two performance levels for each supplier based on the quantity and capability of purchasing from it to be closer to real world problem. The output of this phase is the score of each supplier in each criterion in each level. In the second phase, we propose a nonlinear multi-objective mixed integer model that determines the number and location of all facilities (strategic decision), flow in each echelon of CLSC (tactical decision) and supplier selection and order allocation (hybrid decision). The objective functions maximize profit and scores of suppliers and minimize total pollution. To solve the model, we have created a transformation based on the piecewise linearization method. The mathematical programming model illustrated by a real numerical example.

    Mathematics Subject Classification: Primary: 90B06, 90B50; Secondary: 65K05.


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  • Figure 1.  Proposed supplier selection criteria classification

    Figure 2.  linguistic scale presented by Amin and Razmi [1]

    Figure 3.  Approximation of accumulative standard normal distribution function 6

    Figure 4.  The solution of the numerical example network

    Table 1.  Importance of categories

    CategoryDM1DM2DM3TFN1TFN2TFN3Weight of Category
    AbilityMMMH(3, 5, 7)(3, 5, 7)(5, 7, 9)(3.66, 5.66, 7.66)
    ResponsibilityMHHMH(5, 7, 9)(7, 9, 10)(5, 7, 9)(5.66, 7.66, 9.33)
    GreenHHVH(7, 9, 10)(7, 9, 10)(9, 10, 10)(7.66, 9.33, 10)
    Process-relatedMMHM(3, 5, 7)(5, 7, 9)(3, 5, 7)(3.66, 5.66, 7.66)
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    Table 2.  Importance of criteria

    CriteriaDM1DM2DM3Weight of criteria
    Delivery (Lead time)VHHH(8.33, 9.66, 10)
    Defect rateMHMM(3.66, 5.66, 7.66)
    Financial positionMHMMH(4.33, 6.33, 8.33)
    TrainingHMHVH(7, 8.66, 9.66)
    Number of personnelVHHMH(7, 8.66, 9.66)
    Number of personnelMHMM(3.66, 5.66, 7.66)
    Green packagingMMHMH(4.33, 6.33, 8.33)
    Process flexibilityMMHM(3.66, 5.66, 7.66)
    Process safetyMHHMH(4.33, 6.33, 8.33)
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    Table 3.  Assessment supplier 1 in two performance levels

    Delivery (Lead time)VHHMH(7, 8.66, 9.66)VHVHH(8.33, 9.66, 10)
    Defect rateMHMML(3, 5, 7)HMHM(5, 7, 8.66)
    Financial positionMHMM(3.66, 5.66, 7.66)MHMHM(4.33, 6.33, 8.33)
    TrainingHMHH(6.33, 8.33, 9.66)HHVH(7.66, 9.33, 10)
    Number of personnelVHHMH(7, 8.66, 9.66)VHVHH(8.33, 9.66, 10)
    Number of personnelMHMMH(4.33, 6.33, 8.33)HMHH(6.33, 8.33, 9.66)
    Green packagingMMHM(3.66, 5.66, 7.66)MHHMH(5.66, 7.66, 9.33)
    Process flexibilityMMHMH(4.33, 6.33, 8.33)MHHH(6.33, 8.33, 9.66)
    Process safetyMHHH(6.33, 8.33, 9.66)HVHVH(8.33, 9.66, 10)
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    Table 4.  Final score for supplier 1 in two performance levels

    CriteriaFinal score 1Final score 2a1l1a1l2
    Delivery (Lead time)(213.41,473.49,739.95)(248,462.33,760)411.6490.1
    Defect rate(39.52,160.17,410.72)(64.8,219.52,496.73)203.3260.3
    Financial position(58,202.78,488.76)(66.56,222.26,523.56)249.8270.3
    Number of personnel(277.34,574.46,870.63)(325.36,627.45,892.8)574.1615.1
    Green packaging(117.64,328.1,630.8)(183,445.28,771.9)358.8466.7
    Process flexibility(55.72,197.56,479.4)(81.64,260.28,554.49)244.2298.7
    Process safety(97.52,292.82,605.56)(128.484,292.82,630.8)331.9350.6
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    Table 5.  score of supplier k in criteria l in performance level w

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