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

Masoud Mohammadzadeh; Alireza Arshadi Khamseh; Mohammad Mohammadi

doi:10.3934/jimo.2016061

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April 2017, 13(2): 1041-1064. doi: 10.3934/jimo.2016061

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

Masoud Mohammadzadeh ^, , Alireza Arshadi Khamseh and Mohammad Mohammadi

Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, 15719-14911 Tehran, Iran

* Corresponding author: Masoud Mohammadzadeh

Received July 2015 Revised August 2016 Published October 2016

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.

Keywords: Closed-loop supply chain, uncertain demand, performance level, hybrid motor vehicle, green supplier selection.

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

Citation: Masoud Mohammadzadeh, Alireza Arshadi Khamseh, Mohammad Mohammadi. A multi-objective integrated model for closed-loop supply chain configuration and supplier selection considering uncertain demand and different performance levels. Journal of Industrial & Management Optimization, 2017, 13 (2) : 1041-1064. doi: 10.3934/jimo.2016061

References:

[1]	S. H. Amin and J. Razmi, An integrated fuzzy model for supplier management: A case study of ISP selection and evaluation, Expert Systems with Applications, 36 (2009), 8639-8648. doi: 10.1016/j.eswa.2008.10.012. Google Scholar
[2]	S. H. Amin and G. Zhang, An integrated model for closed-loop supply chain configuration and supplier selection: Multi-objective approach, Expert Systems with Applications, 39 (2012), 6782-6791. doi: 10.1016/j.eswa.2011.12.056. Google Scholar
[3]	A. Azaron, K. N. Brown, S. A. Tarima and M. Modarres, A multi-objective stochastic programming approach for supply chain design considering risk, International Journal of Production Economics, 116 (2008), 129-138. doi: 10.1016/j.ijpe.2008.08.002. Google Scholar
[4]	A. Azaron, K. Furmans and M. Modarres, Interactive multi-objective stochastic programming approaches for designing robust supply chain networks, Operations Research Proceedings 2008, (2009), 173-178. doi: 10.1007/978-3-642-00142-0_28. Google Scholar
[5]	A. Baghalian, S. Rezapour and R. Z. Farahani, Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case, European Journal of Operational Research, 227 (2013), 199-215. doi: 10.1016/j.ejor.2012.12.017. Google Scholar
[6]	L. T. Chen, Dynamic co-opetitive approach of a closed loop system with remanufacturing for deteriorating items in e-markets, Journal of Manufacturing Systems, 33 (2014), 166-176. doi: 10.1016/j.jmsy.2013.11.002. Google Scholar
[7]	S. Y. Chou and Y. H. Chang, A decision support system for supplier selection based on a strategy-aligned fuzzy SMART approac, Expert Systems with Applications, 34 (2008), 2241-2253. Google Scholar
[8]	L. De Boer, E. Labro and P. Morllacchi, A review of methods supporting supplier selection, European Journal of Purchasing and Supply Management, 7 (2001), 75-89. Google Scholar
[9]	H. Fallah, H. Eskandari and M. Pishvaee, Competitive closed-loop supply chain network design under uncertainty, Journal of Manufacturing Systems, 37 (2015), 649-661. doi: 10.1016/j.jmsy.2015.01.005. Google Scholar
[10]	M. Fleischmann, P. Beullens, J. M. Bloemhof-Ruwaard and L. N. Van Wassenhove, The impact of product recovery on logistics network design, Productionand and Operations Management, 10 (2001), 156-173. doi: 10.1111/j.1937-5956.2001.tb00076.x. Google Scholar
[11]	D. Francas and S. Minner, Manufacturing network configuration in supply chains with product recovery, Omega, 37 (2009), 757-769. doi: 10.1016/j.omega.2008.07.007. Google Scholar
[12]	X. Gang, Y. Wuyi and W. Shouyang, Optimal Selection Of Cleaner Products In A Green Supply Chain With Risk Aversion, Journal Of Industrial And Mangement Optimization, 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515. Google Scholar
[13]	S. H. Ghodsypour and C. O'Brein, A decision support system for supplier selection using an integrated analytic hierarchy process and linear programming, International Journal of Production Economics, 56/57 (1998), 199-212. doi: 10.1016/S0925-5273(97)00009-1. Google Scholar
[14]	B. Giri and S. Sharma, Optimizing a closed-loop supply chain with manufacturing defects, Journal of Manufacturing Systems, 35 (2015), 92-111. Google Scholar
[15]	M. Goh, J. Lim and F. Meng, A stochastic model for risk management in global chain networks, European Journal of Operational Research, 182 (2007), 164-173. doi: 10.1016/j.ejor.2006.08.028. Google Scholar
[16]	G. Guillen, F. D. Male, M. J. Bagaajewicz, A. Espuna and L. Puigjaner, Multiobjective supply chain design under uncertainty, Chemical Engineering Science, 60 (2005), 1535-1553. doi: 10.1016/j.ces.2004.10.023. Google Scholar
[17]	I. Harris, M. Naim, A. Palmer, A. Potter and C. Mumdord, Assessing the impact of cost optimization based on infrastructure modelling on CO2 emissions, International Journal of Production Economics, 131 (2011), 313-321. doi: 10.1016/j.ijpe.2010.03.005. Google Scholar
[18]	W. Ho, Integrated analytic hierarchy process and its applications --A literature review, European Journal of Operational Research, 186 (2008), 211-228. doi: 10.1016/j.ejor.2007.01.004. Google Scholar
[19]	P. K. Humphreys, Y. K. Wong and F. T. Chan, Integrating environmental criteria into the supplier selection process, Journal of Materials Processing Technology, 138 (2003), 349-356. doi: 10.1016/S0924-0136(03)00097-9. Google Scholar
[20]	C. L. Hwang and K. Yoon, Multiple Attribute Decision Making: Methods and Applications, Lecture Notes in Economics and Mathematical Systems, 186. Springer-Verlag, Berlin-New York, 1981. Google Scholar
[21]	H. kabza, Hybrid Electric Vehicles: Overview, Encyclopedia of Electrochemical Power Sources, (2009), 249-268. Google Scholar
[22]	C. Kahraman, U. Cebeci and Z. Ulukan, Multi-criteria supplier selection using fuzzy AHP, Logistics Information Management, 16 (2003), 382-394. doi: 10.1108/09576050310503367. Google Scholar
[23]	D. Kannan, R. Khodaverdi, L. Olfat and A. Diabat, Integrated fuzzy multi criteria decision making method and multiobjective programming approach for supplier selection and order allocation in a green supply chain, Journal of Cleaner Production, 47 (2013), 355-367. Google Scholar
[24]	H. J. Ko and G. W. Evans, A genetic-based heuristic for the dynamic integrated forward/reverse logistics network for 3PLs, Computers and Operations Research, 34 (2007), 346-366. doi: 10.1016/j.cor.2005.03.004. Google Scholar
[25]	Y. J. Lai and C. L. Hwang, Fuzzy Mathematical Programming: Methods and Applications, Lecture Notes in Economics and Mathematical Systems, 394. Springer-Verlag, Berlin, 1992. doi: 10.1007/978-3-642-48753-8_3. Google Scholar
[26]	A. H. Lee, H. Y. Kang, C. F. Hsu and H. C. Hung, A green supplier selection model for high-tech industry, Expert Systems with Applications, 36 (2009), 7917-7927. doi: 10.1016/j.eswa.2008.11.052. Google Scholar
[27]	D. H. Lee and M. Dong, Dynamic network design for reverse logistics operations under uncertainty, Transportation Research Part E: Logistics and Transportation Review, 45 (2009), 61-71. doi: 10.1016/j.tre.2008.08.002. Google Scholar
[28]	O. Listes, A generic stochastic model for supply-and-return network design, Computers and Operations Research, 34 (2007), 417-442. doi: 10.1016/j.cor.2005.03.007. Google Scholar
[29]	A. Najla, M. Haouari and E. Hassini, Supplier selection and order lot sizing modeling: A review, Computers and operations research, 34 (2007), 3516-3540. Google Scholar
[30]	K. R. Pati, P. Vrat and P. Kumar, A goal programming model for paper recycling system, Omega, 36 (2008), 405-417. doi: 10.1016/j.omega.2006.04.014. Google Scholar
[31]	S. K. Paul, R. Sarker and D. Essam, Managing risk and disruption in production-inventory and supply chain systems: A review, Journal Of Industrial And Management Optimization, 12 (2016), 1009-1029. doi: 10.3934/jimo.2016.12.1009. Google Scholar
[32]	D. Peidro, J. Mula, R. Poler and J. L. Verdegay, Fuzzy optimization for supply chain planning under supply, demand and process uncertainties, Fuzzy Sets and Systems, 160 (2009), 2640-2657. doi: 10.1016/j.fss.2009.02.021. Google Scholar
[33]	S. pokharel and A. Mutha, Perspectives in reverse logistics: A review, Resources, Conservation and Recycling, 53 (2009), 175-182. doi: 10.1016/j.resconrec.2008.11.006. Google Scholar
[34]	J. Shu and J. Sun, Designing the distribution network for an integrated supply chain, Journal of Industrial and Management Optimization, 2 (2006), 339-349. doi: 10.3934/jimo.2006.2.339. Google Scholar
[35]	B. Sundarakani, R. de'Souza, M. Goh, S. M. Wagner and S. Manikandan, Modeling carbon footprints across the supply chain, International Journal of Production Economics, 128 (2010), 43-50. doi: 10.1016/j.ijpe.2010.01.018. Google Scholar
[36]	M. Thierry, M. Salomon, J. V. Nunen and L. V. Wassenhove, Strategic issues in product recovery management, California Management Review, 37 (1995), 114-135. Google Scholar
[37]	P. Tsiakis, N. Shah and C. C. Pantelides, Design of multi echelon supply chain networks under demand uncertainty, Industrial and Engineering Chemistry Research, 40 (2001), 3585-3604. doi: 10.1021/ie0100030. Google Scholar
[38]	H. Uster, G. Easwaran, E. Akcali and S. Cetinkaya, Benders decomposition with alternative multiple cuts for a multi-product closed-loop supply chain network design model, Naval Research Logistics, 54 (2007), 890-907. doi: 10.1002/nav.20262. Google Scholar
[39]	H. F. Wang and H. W. Hsu, A closed-loop logistic model with a spanning-tree based genetic algorithm, Computers and Operations Research, 37 (2010), 376-389. doi: 10.1016/j.cor.2009.06.001. Google Scholar
[40]	C. A. Weber, J. P. Current and W. C. Benton, Vendor selection criteria and methods, European Journal of Operational Research, 50 (1991), 2-18. doi: 10.1016/0377-2217(91)90033-R. Google Scholar
[41]	G. Xie, W. Yue and S. Wang, Optimal selection of cleaner products in a green supply chain with risk aversion, Journal Of Industrial Aand Management Optimization, 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515. Google Scholar
[42]	Q. Zhai, H. Cao, X. Zhao and C. Yuan, Assessing application potential of clean energy supply for greenhouse gas emission mitigation: a case study on General Motors global manufacturing, Journal of Cleaner Production, 75 (2014), 11-19. doi: 10.1016/j.jclepro.2014.03.072. Google Scholar
[43]	H. Zimmermann, Fuzzy Set Theory And its Applications, Kluwer Academic Publishers, Boston, 2001. doi: 10.1007/978-94-010-0646-0. Google Scholar

show all references

References:

[1]	S. H. Amin and J. Razmi, An integrated fuzzy model for supplier management: A case study of ISP selection and evaluation, Expert Systems with Applications, 36 (2009), 8639-8648. doi: 10.1016/j.eswa.2008.10.012. Google Scholar
[2]	S. H. Amin and G. Zhang, An integrated model for closed-loop supply chain configuration and supplier selection: Multi-objective approach, Expert Systems with Applications, 39 (2012), 6782-6791. doi: 10.1016/j.eswa.2011.12.056. Google Scholar
[3]	A. Azaron, K. N. Brown, S. A. Tarima and M. Modarres, A multi-objective stochastic programming approach for supply chain design considering risk, International Journal of Production Economics, 116 (2008), 129-138. doi: 10.1016/j.ijpe.2008.08.002. Google Scholar
[4]	A. Azaron, K. Furmans and M. Modarres, Interactive multi-objective stochastic programming approaches for designing robust supply chain networks, Operations Research Proceedings 2008, (2009), 173-178. doi: 10.1007/978-3-642-00142-0_28. Google Scholar
[5]	A. Baghalian, S. Rezapour and R. Z. Farahani, Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case, European Journal of Operational Research, 227 (2013), 199-215. doi: 10.1016/j.ejor.2012.12.017. Google Scholar
[6]	L. T. Chen, Dynamic co-opetitive approach of a closed loop system with remanufacturing for deteriorating items in e-markets, Journal of Manufacturing Systems, 33 (2014), 166-176. doi: 10.1016/j.jmsy.2013.11.002. Google Scholar
[7]	S. Y. Chou and Y. H. Chang, A decision support system for supplier selection based on a strategy-aligned fuzzy SMART approac, Expert Systems with Applications, 34 (2008), 2241-2253. Google Scholar
[8]	L. De Boer, E. Labro and P. Morllacchi, A review of methods supporting supplier selection, European Journal of Purchasing and Supply Management, 7 (2001), 75-89. Google Scholar
[9]	H. Fallah, H. Eskandari and M. Pishvaee, Competitive closed-loop supply chain network design under uncertainty, Journal of Manufacturing Systems, 37 (2015), 649-661. doi: 10.1016/j.jmsy.2015.01.005. Google Scholar
[10]	M. Fleischmann, P. Beullens, J. M. Bloemhof-Ruwaard and L. N. Van Wassenhove, The impact of product recovery on logistics network design, Productionand and Operations Management, 10 (2001), 156-173. doi: 10.1111/j.1937-5956.2001.tb00076.x. Google Scholar
[11]	D. Francas and S. Minner, Manufacturing network configuration in supply chains with product recovery, Omega, 37 (2009), 757-769. doi: 10.1016/j.omega.2008.07.007. Google Scholar
[12]	X. Gang, Y. Wuyi and W. Shouyang, Optimal Selection Of Cleaner Products In A Green Supply Chain With Risk Aversion, Journal Of Industrial And Mangement Optimization, 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515. Google Scholar
[13]	S. H. Ghodsypour and C. O'Brein, A decision support system for supplier selection using an integrated analytic hierarchy process and linear programming, International Journal of Production Economics, 56/57 (1998), 199-212. doi: 10.1016/S0925-5273(97)00009-1. Google Scholar
[14]	B. Giri and S. Sharma, Optimizing a closed-loop supply chain with manufacturing defects, Journal of Manufacturing Systems, 35 (2015), 92-111. Google Scholar
[15]	M. Goh, J. Lim and F. Meng, A stochastic model for risk management in global chain networks, European Journal of Operational Research, 182 (2007), 164-173. doi: 10.1016/j.ejor.2006.08.028. Google Scholar
[16]	G. Guillen, F. D. Male, M. J. Bagaajewicz, A. Espuna and L. Puigjaner, Multiobjective supply chain design under uncertainty, Chemical Engineering Science, 60 (2005), 1535-1553. doi: 10.1016/j.ces.2004.10.023. Google Scholar
[17]	I. Harris, M. Naim, A. Palmer, A. Potter and C. Mumdord, Assessing the impact of cost optimization based on infrastructure modelling on CO2 emissions, International Journal of Production Economics, 131 (2011), 313-321. doi: 10.1016/j.ijpe.2010.03.005. Google Scholar
[18]	W. Ho, Integrated analytic hierarchy process and its applications --A literature review, European Journal of Operational Research, 186 (2008), 211-228. doi: 10.1016/j.ejor.2007.01.004. Google Scholar
[19]	P. K. Humphreys, Y. K. Wong and F. T. Chan, Integrating environmental criteria into the supplier selection process, Journal of Materials Processing Technology, 138 (2003), 349-356. doi: 10.1016/S0924-0136(03)00097-9. Google Scholar
[20]	C. L. Hwang and K. Yoon, Multiple Attribute Decision Making: Methods and Applications, Lecture Notes in Economics and Mathematical Systems, 186. Springer-Verlag, Berlin-New York, 1981. Google Scholar
[21]	H. kabza, Hybrid Electric Vehicles: Overview, Encyclopedia of Electrochemical Power Sources, (2009), 249-268. Google Scholar
[22]	C. Kahraman, U. Cebeci and Z. Ulukan, Multi-criteria supplier selection using fuzzy AHP, Logistics Information Management, 16 (2003), 382-394. doi: 10.1108/09576050310503367. Google Scholar
[23]	D. Kannan, R. Khodaverdi, L. Olfat and A. Diabat, Integrated fuzzy multi criteria decision making method and multiobjective programming approach for supplier selection and order allocation in a green supply chain, Journal of Cleaner Production, 47 (2013), 355-367. Google Scholar
[24]	H. J. Ko and G. W. Evans, A genetic-based heuristic for the dynamic integrated forward/reverse logistics network for 3PLs, Computers and Operations Research, 34 (2007), 346-366. doi: 10.1016/j.cor.2005.03.004. Google Scholar
[25]	Y. J. Lai and C. L. Hwang, Fuzzy Mathematical Programming: Methods and Applications, Lecture Notes in Economics and Mathematical Systems, 394. Springer-Verlag, Berlin, 1992. doi: 10.1007/978-3-642-48753-8_3. Google Scholar
[26]	A. H. Lee, H. Y. Kang, C. F. Hsu and H. C. Hung, A green supplier selection model for high-tech industry, Expert Systems with Applications, 36 (2009), 7917-7927. doi: 10.1016/j.eswa.2008.11.052. Google Scholar
[27]	D. H. Lee and M. Dong, Dynamic network design for reverse logistics operations under uncertainty, Transportation Research Part E: Logistics and Transportation Review, 45 (2009), 61-71. doi: 10.1016/j.tre.2008.08.002. Google Scholar
[28]	O. Listes, A generic stochastic model for supply-and-return network design, Computers and Operations Research, 34 (2007), 417-442. doi: 10.1016/j.cor.2005.03.007. Google Scholar
[29]	A. Najla, M. Haouari and E. Hassini, Supplier selection and order lot sizing modeling: A review, Computers and operations research, 34 (2007), 3516-3540. Google Scholar
[30]	K. R. Pati, P. Vrat and P. Kumar, A goal programming model for paper recycling system, Omega, 36 (2008), 405-417. doi: 10.1016/j.omega.2006.04.014. Google Scholar
[31]	S. K. Paul, R. Sarker and D. Essam, Managing risk and disruption in production-inventory and supply chain systems: A review, Journal Of Industrial And Management Optimization, 12 (2016), 1009-1029. doi: 10.3934/jimo.2016.12.1009. Google Scholar
[32]	D. Peidro, J. Mula, R. Poler and J. L. Verdegay, Fuzzy optimization for supply chain planning under supply, demand and process uncertainties, Fuzzy Sets and Systems, 160 (2009), 2640-2657. doi: 10.1016/j.fss.2009.02.021. Google Scholar
[33]	S. pokharel and A. Mutha, Perspectives in reverse logistics: A review, Resources, Conservation and Recycling, 53 (2009), 175-182. doi: 10.1016/j.resconrec.2008.11.006. Google Scholar
[34]	J. Shu and J. Sun, Designing the distribution network for an integrated supply chain, Journal of Industrial and Management Optimization, 2 (2006), 339-349. doi: 10.3934/jimo.2006.2.339. Google Scholar
[35]	B. Sundarakani, R. de'Souza, M. Goh, S. M. Wagner and S. Manikandan, Modeling carbon footprints across the supply chain, International Journal of Production Economics, 128 (2010), 43-50. doi: 10.1016/j.ijpe.2010.01.018. Google Scholar
[36]	M. Thierry, M. Salomon, J. V. Nunen and L. V. Wassenhove, Strategic issues in product recovery management, California Management Review, 37 (1995), 114-135. Google Scholar
[37]	P. Tsiakis, N. Shah and C. C. Pantelides, Design of multi echelon supply chain networks under demand uncertainty, Industrial and Engineering Chemistry Research, 40 (2001), 3585-3604. doi: 10.1021/ie0100030. Google Scholar
[38]	H. Uster, G. Easwaran, E. Akcali and S. Cetinkaya, Benders decomposition with alternative multiple cuts for a multi-product closed-loop supply chain network design model, Naval Research Logistics, 54 (2007), 890-907. doi: 10.1002/nav.20262. Google Scholar
[39]	H. F. Wang and H. W. Hsu, A closed-loop logistic model with a spanning-tree based genetic algorithm, Computers and Operations Research, 37 (2010), 376-389. doi: 10.1016/j.cor.2009.06.001. Google Scholar
[40]	C. A. Weber, J. P. Current and W. C. Benton, Vendor selection criteria and methods, European Journal of Operational Research, 50 (1991), 2-18. doi: 10.1016/0377-2217(91)90033-R. Google Scholar
[41]	G. Xie, W. Yue and S. Wang, Optimal selection of cleaner products in a green supply chain with risk aversion, Journal Of Industrial Aand Management Optimization, 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515. Google Scholar
[42]	Q. Zhai, H. Cao, X. Zhao and C. Yuan, Assessing application potential of clean energy supply for greenhouse gas emission mitigation: a case study on General Motors global manufacturing, Journal of Cleaner Production, 75 (2014), 11-19. doi: 10.1016/j.jclepro.2014.03.072. Google Scholar
[43]	H. Zimmermann, Fuzzy Set Theory And its Applications, Kluwer Academic Publishers, Boston, 2001. doi: 10.1007/978-94-010-0646-0. Google Scholar

Figure 1. Proposed supplier selection criteria classification

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

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Figure 3. Approximation of accumulative standard normal distribution function 6

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Figure 4. The solution of the numerical example network

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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)

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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)

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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
Criteria	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)

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Criteria	SUPPLIER 1 IN LEVEL 1				SUPPLIER 1 IN LEVEL 2
Criteria	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

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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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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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2019 Impact Factor: 1.366

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American Institute of Mathematical Sciences

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

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