Article Contents
Article Contents

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

• 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.

 Citation:

• 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

 Category DM1 DM2 DM3 TFN1 TFN2 TFN3 Weight of Category Ability M M MH (3, 5, 7) (3, 5, 7) (5, 7, 9) (3.66, 5.66, 7.66) Responsibility MH H MH (5, 7, 9) (7, 9, 10) (5, 7, 9) (5.66, 7.66, 9.33) Green H H VH (7, 9, 10) (7, 9, 10) (9, 10, 10) (7.66, 9.33, 10) Process-related M MH M (3, 5, 7) (5, 7, 9) (3, 5, 7) (3.66, 5.66, 7.66)

Table 2.  Importance of criteria

 Criteria DM1 DM2 DM3 Weight of criteria Delivery (Lead time) VH H H (8.33, 9.66, 10) Defect rate MH M M (3.66, 5.66, 7.66) Financial position MH M MH (4.33, 6.33, 8.33) Training H MH VH (7, 8.66, 9.66) Number of personnel VH H MH (7, 8.66, 9.66) Number of personnel MH M M (3.66, 5.66, 7.66) Green packaging M MH MH (4.33, 6.33, 8.33) Process flexibility M MH M (3.66, 5.66, 7.66) Process safety MH H MH (4.33, 6.33, 8.33)

Table 3.  Assessment supplier 1 in two performance levels

 Criteria SUPPLIER 1 IN LEVEL 1 SUPPLIER 1 IN LEVEL 2 DM1 DM2 DM3 ASSESSMENT SUPPLIER 1 IN LEVEL 1 DM1 DM2 DM3 ASSESSMENT SUPPLIER 1 IN LEVEL 2 Delivery (Lead time) VH H MH (7, 8.66, 9.66) VH VH H (8.33, 9.66, 10) Defect rate MH M ML (3, 5, 7) H MH M (5, 7, 8.66) Financial position MH M M (3.66, 5.66, 7.66) MH MH M (4.33, 6.33, 8.33) Training H MH H (6.33, 8.33, 9.66) H H VH (7.66, 9.33, 10) Number of personnel VH H MH (7, 8.66, 9.66) VH VH H (8.33, 9.66, 10) Number of personnel MH M MH (4.33, 6.33, 8.33) H MH H (6.33, 8.33, 9.66) Green packaging M MH M (3.66, 5.66, 7.66) MH H MH (5.66, 7.66, 9.33) Process flexibility M MH MH (4.33, 6.33, 8.33) MH H H (6.33, 8.33, 9.66) Process safety MH H H (6.33, 8.33, 9.66) H VH VH (8.33, 9.66, 10)

Table 4.  Final score for supplier 1 in two performance levels

 Criteria Final score 1 Final score 2 a1l1 a1l2 Delivery (Lead time) (213.41,473.49,739.95) (248,462.33,760) 411.6 490.1 Defect rate (39.52,160.17,410.72) (64.8,219.52,496.73) 203.3 260.3 Financial position (58,202.78,488.76) (66.56,222.26,523.56) 249.8 270.3 Training (250.79,552.57,870.63) (297.92,607.84,892.8) 557.9 599.5 Number of personnel (277.34,574.46,870.63) (325.36,627.45,892.8) 574.1 615.1 Reusable (121.39,328.1,630.8) (172.36,432.26,729.6) 360 444.7 Green packaging (117.64,328.1,630.8) (183,445.28,771.9) 358.8 466.7 Process flexibility (55.72,197.56,479.4) (81.64,260.28,554.49) 244.2 298.7 Process safety (97.52,292.82,605.56) (128.484,292.82,630.8) 331.9 350.6

Table 5.  score of supplier k in criteria l in performance level w

 aklw k1 k2 k3 k4 k5 l1.w1 411.6 372.5 367.7 433.4 371.1 l2.w1 203.3 505.9 563 270.2 288.1 l3.w1 249.8 420.6 499.4 525.2 473.7 l4.w1 557.9 425.8 345.8 248.1 478.4 l5.w1 574.1 410.9 505.6 383.2 573.7 l6.w1 360 225.6 561.3 491 384.1 l7.w1 358.8 523.9 232.9 280.4 366.7 l8.w1 244.2 217.6 300.8 477.9 307.8 l9.w1 331.9 204.7 234.2 533.9 283.9 l1.w2 490.1 409.7 404.4 476.7 408.2 l2.w2 260.3 556.4 619.3 297.2 316.9 l3.w2 270.3 462.6 549.3 577.7 521.1 l4.w2 599.5 638.7 518.7 372.1 717.6 l5.w2 615.1 616.3 758.4 574.8 860.5 l6.w2 444.7 239.1 594.9 520.4 407.1 l7.w2 466.7 555.3 246.8 297.2 388.7 l8.w2 298.7 243.7 336.8 535.2 344.7 l9.w2 350.6 229.2 262.3 597.9 317.9
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Tables(5)