# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2022057
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## Designing a multi-echelon closed-loop supply chain with disruption in the distribution centers under uncertainty

 1 Department of Industrial Engineering, Nour Branch, Islamic Azad University, Nour, Iran 2 Department of Industrial Engineering and Quality Research Centre, Nour Branch, Islamic Azad University, Nour, Iran 3 Department of Industrial Engineering, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran 4 Innovation and Management Research Center, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran

*Corresponding author: Fatemeh Harsej

Received  April 2021 Revised  February 2022 Early access April 2022

According to the need for further cost reduction and improving the process of the organization in the direction of customer demand, the concept of the supply chain has become increasingly significant and the organizations seek to expand this concept within their organizational framework. In this regard, efficient planning of distribution of products in the supply chain by considering disruption has received more attention recently. In this study a multi-objective mixed-integer linear programming model is developed for a green multi-echelon closed-loop supply chain network design under uncertainty. Moreover, a partial disruption is considered for distribution centers where has not been studied enough in previous works. The fuzzy credibility constraint approach is applied to cover uncertainty. In the following, the ε-constraint method is presented to solve and validate the model in small-sized instances. Moreover, a Non-dominated Sorting Genetic Algorithm is developed for solving the large-sized problems. Results show that uncertainty has a crucial impact on objective functions where the increase of objective functions by increasing the level of uncertainty, which was observed in all categories. Furthermore, the proposed NSGA-Ⅱ is the best tool to deal with large-size problems where the EC method lacks the necessary efficiency.

Citation: Kaveh Keshmiry Zadeh, Fatemeh Harsej, Mahboubeh Sadeghpour, Mohammad Molani Aghdam. Designing a multi-echelon closed-loop supply chain with disruption in the distribution centers under uncertainty. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022057
##### References:
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Balin, Parallel machine scheduling with fuzzy processing times using a robust genetic algorithm and simulation, Information Sciences, 181 (2011), 3551-3569.  doi: 10.1016/j.ins.2011.04.010. [6] J. Behnamian and S. F. Ghomi, Multi-objective fuzzy multiprocessor flowshop scheduling, Applied Soft Computing, 21 (2014), 139-148.  doi: 10.1016/j.asoc.2014.03.031. [7] A. Diabat, A. Jabbarzadeh and A. Khosrojerdi, A perishable product supply chain network design problem with reliability and disruption considerations, International J. Production Economics, 212 (2019), 125-138.  doi: 10.1016/j.ijpe.2018.09.018. [8] M. Fattahi, K. Govindan and E. Keyvanshokooh, Responsive and resilient supply chain network design under operational and disruption risks with delivery lead-time sensitive customers, Transportation Research Part E: Logistics and Transportation Review, 101 (2017), 176-200.  doi: 10.1016/j.tre.2017.02.004. [9] M. Ghomi-Avili, S. G. J. Naeini, R. Tavakkoli-Moghaddam and A. Jabbarzadeh, A fuzzy pricing model for a green competitive closed-loop supply chain network design in the presence of disruptions, J. Cleaner Production, 188 (2018), 425-442.  doi: 10.1016/j.jclepro.2018.03.273. [10] V. Gupta and A. Chutani, Supply chain financing with advance selling under disruption, Int. Trans. Oper. Res., 27 (2020), 2449-2468.  doi: 10.1111/itor.12663. [11] B. Hamdan and A. Diabat, Robust design of blood supply chains under risk of disruptions using Lagrangian relaxation, Transportation Research Part E: Logistics and Transportation Review, 134 (2020), 101764.  doi: 10.1016/j.tre.2019.08.005. [12] M. Hapke and R. Slowinski, Scheduling Under Fuzziness, Physica-Verlag. [13] A. Hasani and A. Khosrojerdi, Robust global supply chain network design under disruption and uncertainty considering resilience strategies: A parallel memetic algorithm for a real-life case study, Transportation Research Part E: Logistics and Transportation Review, 87 (2016), 20-52.  doi: 10.1016/j.tre.2015.12.009. [14] S. M. Hatefi and F. Jolai, Robust and reliable forward-reverse logistics network design under demand uncertainty and facility disruptions, Appl. Math. Model., 38 (2014), 2630-2647.  doi: 10.1016/j.apm.2013.11.002. [15] S. M. Hatefi and F. Jolai, Reliable forward-reverse logistics network design under partial and complete facility disruptions, International J. Logistics Systems and Management, 20 (2015), 370-394.  doi: 10.1504/IJLSM.2015.068426. [16] S. M. Hatefi, F. Jolai, S. A. Torabi and R. Tavakkoli-Moghaddam, Reliable design of an integrated forward-revere logistics network under uncertainty and facility disruptions: A fuzzy possibilistic programing model, KSCE Journal of Civil Engineering, 19 (2015), 1117-1128.  doi: 10.1007/s12205-013-0340-y. [17] S. M. Hatefi, F. Jolai, S. A. Torabi and R. Tavakkoli-Moghaddam, A credibility-constrained programming for reliable forward-reverse logistics network design under uncertainty and facility disruptions, International J. Computer Integrated Manufacturing, 28 (2015), 664-678.  doi: 10.1080/0951192X.2014.900863. [18] J. Heydari, P. Zaabi-Ahmadi and T. M. Choi, Coordinating supply chains with stochastic demand by crashing lead times, Comput. Oper. Res., 100 (2018), 394-403.  doi: 10.1016/j.cor.2016.10.009. [19] D. Ivanov, A. Pavlov, D. Pavlov and B. Sokolov, Minimization of disruption-related return flows in the supply chain, International J. Production Economics, 183 (2017), 503-513.  doi: 10.1016/j.ijpe.2016.03.012. [20] A. Jabbarzadeh, M. Haughton and A. Khosrojerdi, Closed-loop supply chain network design under disruption risks: A robust approach with real world application, Computers and Industrial Engineering, 116 (2018), 178-191.  doi: 10.1016/j.cie.2017.12.025. [21] R. Jamshidi, S. F. Ghomi and B. Karimi, Multi-objective green supply chain optimization with a new hybrid memetic algorithm using the Taguchi method, Scientia Iranica, 19 (2012), 1876-1886.  doi: 10.1016/j.scient.2012.07.002. [22] V. Kayvanfar, S. M. Husseini, B. Karimi and M. S. Sajadieh, Bi-objective intelligent water drops algorithm to a practical multi-echelon supply chain optimization problem, J. Manufacturing Systems, 44, 93–114. [23] M. Keshavarz Ghorabaee, M. Amiri, L. Olfat and S. A. Khatami Firouzabadi, Designing a multi-product multi-period supply chain network with reverse logistics and multiple objectives under uncertainty, Technological and Economic Development of Economy, 23, 520–548. [24] E. Khanmohammadi, H. Safari, M. Zandieh, B. Malmir and E. B. Tirkolaee, Development of dynamic balanced scorecard using case-based reasoning method and adaptive neuro-fuzzy inference system, IEEE Transactions on Engineering Management, (2022), 1–4. doi: 10.1109/TEM.2022.3140291. [25] R. S. Kumar, A. Choudhary, S. A. Babu, S. K. Kumar, A. Goswami and M. K. Tiwari, Designing multi-period supply chain network considering risk and emission: A multi-objective approach, Ann. Oper. Res., 250 (2017), 427-461.  doi: 10.1007/s10479-015-2086-z. [26] X. Li and B. Liu, A sufficient and necessary condition for credibility measures, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, 14 (2006), 527-535.  doi: 10.1142/S0218488506004175. [27] Y. F. Li and W. F. Jia, Supply chain coordination with considering defective quality products cheaply processing understochastic demand, J. Residuals Science and Technology, 13, 731–737. [28] B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE transactions on Fuzzy Systems, 10, 445–450. [29] D. Liu, Uncertainty Theory, 4$^{th}$ edition, Springer Uncertainty Research. Springer, Heidelberg, 2015. doi: 10.1007/978-3-662-44354-5. [30] Y. Liu, L. Ma and Y. Liu, A novel robust fuzzy mean-UPM model for green closed-loop supply chain network design under distribution ambiguity, Appl. Math. Model., 92 (2021), 99-135.  doi: 10.1016/j.apm.2020.10.042. [31] F. Lücker, R. W. Seifert and I. Biçer, Roles of inventory and reserve capacity in mitigating supply chain disruption risk, International Journal of Production Research, 57 (2019), 1238-1249.  doi: 10.1080/00207543.2018.1504173. [32] G. Mavrotas, Effective implementation of the E-constraint method in multi-objective mathematical programming problems, Appl. Math. Comput., 213 (2009), 455-465.  doi: 10.1016/j.amc.2009.03.037. [33] A. Niknejad and D. Petrovic, Optimisation of integrated reverse logistics networks with different product recovery routes, European J. Oper. Res., 238 (2014), 143-154.  doi: 10.1016/j.ejor.2014.03.034. [34] A. Nobari, S. Kheirkhah and M. Esmaeili, Considering pricing problem in a dynamic and integrated design of sustainable closed-loop supply chain network, International J. Industrial Engineering and Production Research, 27, 353–371. [35] M. NoParast, M. Hematian, A. Ashrafian, M. J. T. Amiri and H. AzariJafari, Development of a non-dominated sorting genetic algorithm for implementing circular economy strategies in the concrete industry, Sustainable Production and Consumption, 27 (2021), 933-946.  doi: 10.1016/j.spc.2021.02.009. [36] E. Özceylan and T. Paksoy, A mixed integer programming model for a closed-loop supply-chain network, International J. Production Research, 51, 718–734. [37] S. Pal and G. S. Mahapatra, A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages, Computers and Industrial Engineering, 106 (2017), 299-314.  doi: 10.1016/j.cie.2017.02.003. [38] S. H. R. Pasandideh, S. T. A. Niaki and K. Asadi, Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-Ⅱ and NRGA, Inform. Sci., 292 (2015), 57-74.  doi: 10.1016/j.ins.2014.08.068. [39] S. H. R. Pasandideh, S. T. A. Niaki and K. Asadi, Optimizing a bi-objective multi-product multi-period three echelon supply chain network with warehouse reliability, Expert Systems with Applications, 42, 2615–2623. [40] M. S. Pishvaee and J. Razmi, Environmental supply chain network design using multi-objective fuzzy mathematical programming, Appl. Math. Model., 36 (2012), 3433-3446.  doi: 10.1016/j.apm.2011.10.007. [41] M. Ramezani, A. M. Kimiagari and B. Karimi, Closed-loop supply chain network design: A financial approach, Appl. Math. Model., 38 (2014), 4099-4119.  doi: 10.1016/j.apm.2014.02.004. [42] S. Sadeghi, H. Saffari and N. Bahadormanesh, Optimization of a modified double-turbine Kalina cycle by using Artificial Bee Colony algorithm, Applied Thermal Engineering, 91 (2015), 19-32.  doi: 10.1016/j.applthermaleng.2015.08.014. [43] T. Sawik, A Multi-portfolio Approach to Integrated Risk-Averse Planning in Supply Chains Under Disruption Risks, Handbook of Ripple Effects in the Supply Chain, 276 (2019), 35-63.  doi: 10.1007/978-3-030-14302-2_2. [44] E. Teimuory, F. Atoei, E. Mohammadi and A. Amiri, A multi-objective reliable programming model for disruption in supply chain, Management Science Letters, 3 (2013), 1467-1478.  doi: 10.5267/j.msl.2013.03.028. [45] E. B. Tirkolaee and N. S. Aydin, Integrated design of sustainable supply chain and transportation network using a fuzzy bi-level decision support system for perishable products, Expert Systems with Applications, 195 (2020), 116628.  doi: 10.1016/j.eswa.2022.116628. [46] E. B. Tirkolaee, A. Goli, S. Gütmen, G. W. Weber and K. Szwedzka, A novel model for sustainable waste collection arc routing problem: Pareto-based algorithms, Annals of Operations Research. [47] M. Yavari, H. Enjavi and M. Geraeli, Demand management to cope with routes disruptions in location-inventory-routing problem for perishable products, Research in Transportation Business and Management, 37 (2020), 100552.  doi: 10.1016/j.rtbm.2020.100552. [48] M. Yavari and H. Zaker, Designing a resilient-green closed loop supply chain network for perishable products by considering disruption in both supply chain and power networks, Computers and Chemical Engineering, 134 (2020), 106680.  doi: 10.1016/j.compchemeng.2019.106680. [49] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.  doi: 10.1016/S0019-9958(65)90241-X. [50] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1 (1978), 3-28.  doi: 10.1016/0165-0114(78)90029-5. [51] Y. Zhang, A. Diabat and Z. H. Zhang, Reliable closed-loop supply chain design problem under facility-type-dependent probabilistic disruptions, Transportation Research Part B: Methodological, 146 (2021), 180-209.  doi: 10.1016/j.trb.2021.02.009. [52] H. Zhu and J. Zhang, A credibility-based fuzzy programming model for APP problem, International Conference on Artificial Intelligence and Computational Intelligence, 1 (2009), 455-459.  doi: 10.1109/AICI.2009.204. [53] H. J. Zimmermann, Fuzzy set theory, WIREs Computational Statistics, 2 (2010), 317-332.  doi: 10.1002/wics.82.

show all references

##### References:
 [1] M. A. Alhaj, D. Svetinovic and A. Diabat, Retracted: A carbon-sensitive two-echelon-inventory supply chain model with stochastic demand, Resources, Conservation and Recycling, 108 (2016), 82-87.  doi: 10.1016/j.resconrec.2015.11.011. [2] M. Alinezhad, I. Mahdavi, M. Hematian and E. B. Tirkolaee, A fuzzy multi-objective optimization model for sustainable closed-loop supply chain network design in food industries, Environment, Development and Sustainability, (2021). doi: 10.1007/s10668-021-01809-y. [3] F. Atoei, E. Teimory and A. Amiri, Designing reliable supply chain network with disruption risk, International J. Industrial Engineering Computations, 4, 111–126. [4] N. Azad, G. K. Saharidis, H. Davoudpour, H. Malekly and S. A. Yektamaram, Strategies for protecting supply chain networks against facility and transportation disruptions: An improved Benders decomposition approach, Ann. Oper. Res., 210 (2013), 125-163.  doi: 10.1007/s10479-012-1146-x. [5] S. Balin, Parallel machine scheduling with fuzzy processing times using a robust genetic algorithm and simulation, Information Sciences, 181 (2011), 3551-3569.  doi: 10.1016/j.ins.2011.04.010. [6] J. Behnamian and S. F. Ghomi, Multi-objective fuzzy multiprocessor flowshop scheduling, Applied Soft Computing, 21 (2014), 139-148.  doi: 10.1016/j.asoc.2014.03.031. [7] A. Diabat, A. Jabbarzadeh and A. Khosrojerdi, A perishable product supply chain network design problem with reliability and disruption considerations, International J. Production Economics, 212 (2019), 125-138.  doi: 10.1016/j.ijpe.2018.09.018. [8] M. Fattahi, K. Govindan and E. Keyvanshokooh, Responsive and resilient supply chain network design under operational and disruption risks with delivery lead-time sensitive customers, Transportation Research Part E: Logistics and Transportation Review, 101 (2017), 176-200.  doi: 10.1016/j.tre.2017.02.004. [9] M. Ghomi-Avili, S. G. J. Naeini, R. Tavakkoli-Moghaddam and A. Jabbarzadeh, A fuzzy pricing model for a green competitive closed-loop supply chain network design in the presence of disruptions, J. Cleaner Production, 188 (2018), 425-442.  doi: 10.1016/j.jclepro.2018.03.273. [10] V. Gupta and A. Chutani, Supply chain financing with advance selling under disruption, Int. Trans. Oper. Res., 27 (2020), 2449-2468.  doi: 10.1111/itor.12663. [11] B. Hamdan and A. Diabat, Robust design of blood supply chains under risk of disruptions using Lagrangian relaxation, Transportation Research Part E: Logistics and Transportation Review, 134 (2020), 101764.  doi: 10.1016/j.tre.2019.08.005. [12] M. Hapke and R. Slowinski, Scheduling Under Fuzziness, Physica-Verlag. [13] A. Hasani and A. Khosrojerdi, Robust global supply chain network design under disruption and uncertainty considering resilience strategies: A parallel memetic algorithm for a real-life case study, Transportation Research Part E: Logistics and Transportation Review, 87 (2016), 20-52.  doi: 10.1016/j.tre.2015.12.009. [14] S. M. Hatefi and F. Jolai, Robust and reliable forward-reverse logistics network design under demand uncertainty and facility disruptions, Appl. Math. Model., 38 (2014), 2630-2647.  doi: 10.1016/j.apm.2013.11.002. [15] S. M. Hatefi and F. Jolai, Reliable forward-reverse logistics network design under partial and complete facility disruptions, International J. Logistics Systems and Management, 20 (2015), 370-394.  doi: 10.1504/IJLSM.2015.068426. [16] S. M. Hatefi, F. Jolai, S. A. Torabi and R. Tavakkoli-Moghaddam, Reliable design of an integrated forward-revere logistics network under uncertainty and facility disruptions: A fuzzy possibilistic programing model, KSCE Journal of Civil Engineering, 19 (2015), 1117-1128.  doi: 10.1007/s12205-013-0340-y. [17] S. M. Hatefi, F. Jolai, S. A. Torabi and R. Tavakkoli-Moghaddam, A credibility-constrained programming for reliable forward-reverse logistics network design under uncertainty and facility disruptions, International J. Computer Integrated Manufacturing, 28 (2015), 664-678.  doi: 10.1080/0951192X.2014.900863. [18] J. Heydari, P. Zaabi-Ahmadi and T. M. Choi, Coordinating supply chains with stochastic demand by crashing lead times, Comput. Oper. Res., 100 (2018), 394-403.  doi: 10.1016/j.cor.2016.10.009. [19] D. Ivanov, A. Pavlov, D. Pavlov and B. Sokolov, Minimization of disruption-related return flows in the supply chain, International J. Production Economics, 183 (2017), 503-513.  doi: 10.1016/j.ijpe.2016.03.012. [20] A. Jabbarzadeh, M. Haughton and A. Khosrojerdi, Closed-loop supply chain network design under disruption risks: A robust approach with real world application, Computers and Industrial Engineering, 116 (2018), 178-191.  doi: 10.1016/j.cie.2017.12.025. [21] R. Jamshidi, S. F. Ghomi and B. Karimi, Multi-objective green supply chain optimization with a new hybrid memetic algorithm using the Taguchi method, Scientia Iranica, 19 (2012), 1876-1886.  doi: 10.1016/j.scient.2012.07.002. [22] V. Kayvanfar, S. M. Husseini, B. Karimi and M. S. Sajadieh, Bi-objective intelligent water drops algorithm to a practical multi-echelon supply chain optimization problem, J. Manufacturing Systems, 44, 93–114. [23] M. Keshavarz Ghorabaee, M. Amiri, L. Olfat and S. A. Khatami Firouzabadi, Designing a multi-product multi-period supply chain network with reverse logistics and multiple objectives under uncertainty, Technological and Economic Development of Economy, 23, 520–548. [24] E. Khanmohammadi, H. Safari, M. Zandieh, B. Malmir and E. B. Tirkolaee, Development of dynamic balanced scorecard using case-based reasoning method and adaptive neuro-fuzzy inference system, IEEE Transactions on Engineering Management, (2022), 1–4. doi: 10.1109/TEM.2022.3140291. [25] R. S. Kumar, A. Choudhary, S. A. Babu, S. K. Kumar, A. Goswami and M. K. Tiwari, Designing multi-period supply chain network considering risk and emission: A multi-objective approach, Ann. Oper. Res., 250 (2017), 427-461.  doi: 10.1007/s10479-015-2086-z. [26] X. Li and B. Liu, A sufficient and necessary condition for credibility measures, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, 14 (2006), 527-535.  doi: 10.1142/S0218488506004175. [27] Y. F. Li and W. F. Jia, Supply chain coordination with considering defective quality products cheaply processing understochastic demand, J. Residuals Science and Technology, 13, 731–737. [28] B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE transactions on Fuzzy Systems, 10, 445–450. [29] D. Liu, Uncertainty Theory, 4$^{th}$ edition, Springer Uncertainty Research. Springer, Heidelberg, 2015. doi: 10.1007/978-3-662-44354-5. [30] Y. Liu, L. Ma and Y. Liu, A novel robust fuzzy mean-UPM model for green closed-loop supply chain network design under distribution ambiguity, Appl. Math. Model., 92 (2021), 99-135.  doi: 10.1016/j.apm.2020.10.042. [31] F. Lücker, R. W. Seifert and I. Biçer, Roles of inventory and reserve capacity in mitigating supply chain disruption risk, International Journal of Production Research, 57 (2019), 1238-1249.  doi: 10.1080/00207543.2018.1504173. [32] G. Mavrotas, Effective implementation of the E-constraint method in multi-objective mathematical programming problems, Appl. Math. Comput., 213 (2009), 455-465.  doi: 10.1016/j.amc.2009.03.037. [33] A. Niknejad and D. Petrovic, Optimisation of integrated reverse logistics networks with different product recovery routes, European J. Oper. Res., 238 (2014), 143-154.  doi: 10.1016/j.ejor.2014.03.034. [34] A. Nobari, S. Kheirkhah and M. Esmaeili, Considering pricing problem in a dynamic and integrated design of sustainable closed-loop supply chain network, International J. Industrial Engineering and Production Research, 27, 353–371. [35] M. NoParast, M. Hematian, A. Ashrafian, M. J. T. Amiri and H. AzariJafari, Development of a non-dominated sorting genetic algorithm for implementing circular economy strategies in the concrete industry, Sustainable Production and Consumption, 27 (2021), 933-946.  doi: 10.1016/j.spc.2021.02.009. [36] E. Özceylan and T. Paksoy, A mixed integer programming model for a closed-loop supply-chain network, International J. Production Research, 51, 718–734. [37] S. Pal and G. S. Mahapatra, A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages, Computers and Industrial Engineering, 106 (2017), 299-314.  doi: 10.1016/j.cie.2017.02.003. [38] S. H. R. Pasandideh, S. T. A. Niaki and K. Asadi, Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-Ⅱ and NRGA, Inform. Sci., 292 (2015), 57-74.  doi: 10.1016/j.ins.2014.08.068. [39] S. H. R. Pasandideh, S. T. A. Niaki and K. Asadi, Optimizing a bi-objective multi-product multi-period three echelon supply chain network with warehouse reliability, Expert Systems with Applications, 42, 2615–2623. [40] M. S. Pishvaee and J. Razmi, Environmental supply chain network design using multi-objective fuzzy mathematical programming, Appl. Math. Model., 36 (2012), 3433-3446.  doi: 10.1016/j.apm.2011.10.007. [41] M. Ramezani, A. M. Kimiagari and B. Karimi, Closed-loop supply chain network design: A financial approach, Appl. Math. Model., 38 (2014), 4099-4119.  doi: 10.1016/j.apm.2014.02.004. [42] S. Sadeghi, H. Saffari and N. Bahadormanesh, Optimization of a modified double-turbine Kalina cycle by using Artificial Bee Colony algorithm, Applied Thermal Engineering, 91 (2015), 19-32.  doi: 10.1016/j.applthermaleng.2015.08.014. [43] T. Sawik, A Multi-portfolio Approach to Integrated Risk-Averse Planning in Supply Chains Under Disruption Risks, Handbook of Ripple Effects in the Supply Chain, 276 (2019), 35-63.  doi: 10.1007/978-3-030-14302-2_2. [44] E. Teimuory, F. Atoei, E. Mohammadi and A. Amiri, A multi-objective reliable programming model for disruption in supply chain, Management Science Letters, 3 (2013), 1467-1478.  doi: 10.5267/j.msl.2013.03.028. [45] E. B. Tirkolaee and N. S. Aydin, Integrated design of sustainable supply chain and transportation network using a fuzzy bi-level decision support system for perishable products, Expert Systems with Applications, 195 (2020), 116628.  doi: 10.1016/j.eswa.2022.116628. [46] E. B. Tirkolaee, A. Goli, S. Gütmen, G. W. Weber and K. Szwedzka, A novel model for sustainable waste collection arc routing problem: Pareto-based algorithms, Annals of Operations Research. [47] M. Yavari, H. Enjavi and M. Geraeli, Demand management to cope with routes disruptions in location-inventory-routing problem for perishable products, Research in Transportation Business and Management, 37 (2020), 100552.  doi: 10.1016/j.rtbm.2020.100552. [48] M. Yavari and H. Zaker, Designing a resilient-green closed loop supply chain network for perishable products by considering disruption in both supply chain and power networks, Computers and Chemical Engineering, 134 (2020), 106680.  doi: 10.1016/j.compchemeng.2019.106680. [49] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.  doi: 10.1016/S0019-9958(65)90241-X. [50] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1 (1978), 3-28.  doi: 10.1016/0165-0114(78)90029-5. [51] Y. Zhang, A. Diabat and Z. H. Zhang, Reliable closed-loop supply chain design problem under facility-type-dependent probabilistic disruptions, Transportation Research Part B: Methodological, 146 (2021), 180-209.  doi: 10.1016/j.trb.2021.02.009. [52] H. Zhu and J. Zhang, A credibility-based fuzzy programming model for APP problem, International Conference on Artificial Intelligence and Computational Intelligence, 1 (2009), 455-459.  doi: 10.1109/AICI.2009.204. [53] H. J. Zimmermann, Fuzzy set theory, WIREs Computational Statistics, 2 (2010), 317-332.  doi: 10.1002/wics.82.
Distribution center and Customer relation considering disruption
The proposed CLSC
Trapezoidal fuzzy numbers
The Figure of possibility function of trapezoidal fuzzy number
The Figure of necessity function of trapezoidal fuzzy number
The Figure of credibility function of trapezoidal fuzzy number
An example of chromosome
Interpretation of chromosome
Obtained solutions by NSGA-Ⅱ and EC
The comparison of NSGA-Ⅱ and EC at confidence level 0.5
The comparison of NSGA-Ⅱ and EC at confidence level 0.7
The comparison of NSGA-Ⅱ and EC at confidence level 0.9
The comparison of solution time for NSGA-Ⅱ and EC
Summary of research in CLSC
 Researchers Year Supply chain Objective Modeling approach Solution approach Uncertainty Disruption Forward Reverse Forward and reverse Closed-loop Single Multiple Deterministic Stochastic Fuzzy Random-robust Exact Heuristic Meta-heuristic Demand Other parameters Equipment Distribution center Other centers Azad et al.[4] 2013 ✓ ✓ ✓ ✓ ✓ ✓ Atoei Bozorgi et al.[3] 2013 ✓ ✓ ✓ ✓ ✓ ✓ Teimuory et al.[44] 2013 ✓ ✓ ✓ ✓ ✓ ✓ ✓ Hatefi & Jolai[14] 2014 ✓ ✓ ✓ ✓ ✓ ✓ Hatefi et al.[17] 2015 ✓ ✓ ✓ ✓ ✓ ✓ Hatefi & Jolai[15] 2015 ✓ ✓ ✓ ✓ ✓ Hatefi et al.[16] 2015 ✓ ✓ ✓ ✓ ✓ ✓ Hasani & Khosrojerdi[13] 2016 ✓ ✓ ✓ ✓ ✓ ✓ ✓ Ivanov et al.[19] 2017 ✓ ✓ ✓ ✓ ✓ Jabbarzadeh et al.[20] 2018 ✓ ✓ ✓ ✓ ✓ Yavari & Zaker[48] 2020 ✓ ✓ ✓ ✓ ✓ Zhang et al.[51] 2021 ✓ ✓ ✓ ✓ ✓ ✓ Current work 2022 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
 Researchers Year Supply chain Objective Modeling approach Solution approach Uncertainty Disruption Forward Reverse Forward and reverse Closed-loop Single Multiple Deterministic Stochastic Fuzzy Random-robust Exact Heuristic Meta-heuristic Demand Other parameters Equipment Distribution center Other centers Azad et al.[4] 2013 ✓ ✓ ✓ ✓ ✓ ✓ Atoei Bozorgi et al.[3] 2013 ✓ ✓ ✓ ✓ ✓ ✓ Teimuory et al.[44] 2013 ✓ ✓ ✓ ✓ ✓ ✓ ✓ Hatefi & Jolai[14] 2014 ✓ ✓ ✓ ✓ ✓ ✓ Hatefi et al.[17] 2015 ✓ ✓ ✓ ✓ ✓ ✓ Hatefi & Jolai[15] 2015 ✓ ✓ ✓ ✓ ✓ Hatefi et al.[16] 2015 ✓ ✓ ✓ ✓ ✓ ✓ Hasani & Khosrojerdi[13] 2016 ✓ ✓ ✓ ✓ ✓ ✓ ✓ Ivanov et al.[19] 2017 ✓ ✓ ✓ ✓ ✓ Jabbarzadeh et al.[20] 2018 ✓ ✓ ✓ ✓ ✓ Yavari & Zaker[48] 2020 ✓ ✓ ✓ ✓ ✓ Zhang et al.[51] 2021 ✓ ✓ ✓ ✓ ✓ ✓ Current work 2022 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
The value of parameters for NSGA-Ⅱ
 Parameter Value Npop 50 80 100 Max_iteration 100 200 300 Cross_rate 0.5 0.7 0.9 Mut_rate 0.5 0.3 0.1
 Parameter Value Npop 50 80 100 Max_iteration 100 200 300 Cross_rate 0.5 0.7 0.9 Mut_rate 0.5 0.3 0.1
The optimal value of parameters of NSGA-Ⅱ
 Parameter Value Npop 100 Max_iteration 200 Cross_rate 0.7 Mut_rate 0.3
 Parameter Value Npop 100 Max_iteration 200 Cross_rate 0.7 Mut_rate 0.3
Sample problem
 Indices Definition Number s Supply center 2 m Production center 3 j Distribution center 3 k Customers 4 c Collection center 2 o Recovery center 2 d Disposal center 1 r Unsafe transport mode between distribution centers and customers 2
 Indices Definition Number s Supply center 2 m Production center 3 j Distribution center 3 k Customers 4 c Collection center 2 o Recovery center 2 d Disposal center 1 r Unsafe transport mode between distribution centers and customers 2
The fuzzy demand of customers
 Customers Fuzzy demand a b c d 1 180 150 130 100 2 300 260 220 200 3 240 210 180 150 4 390 360 340 300
 Customers Fuzzy demand a b c d 1 180 150 130 100 2 300 260 220 200 3 240 210 180 150 4 390 360 340 300
The fuzzy transportation cost between reliable and unreliable distribution centers $\left(uc_{ij}\right)\left({}^\star100\right)$
 Reliable distribution centers Unreliable distribution centers 1 2 3 a b c d a b c d a b c d 1 - - - - 15 14 13 12 18 17 16 15 2 13 12 11 10 - - - - 17 16 15 14 3 15 14 13 12 17 16 15 14 - - - -
 Reliable distribution centers Unreliable distribution centers 1 2 3 a b c d a b c d a b c d 1 - - - - 15 14 13 12 18 17 16 15 2 13 12 11 10 - - - - 17 16 15 14 3 15 14 13 12 17 16 15 14 - - - -
The information of input parameters
 Parameter Uniform distribution Parameter Uniform distribution $tcd_{cd}$ $\sim U(8, 20)$ $sm_m$ $\sim U(900, 2000)$ $tco_{om}$ $\sim U(10, 20)$ $sc_c$ $\sim U(1500, 2500)$ $pcap_m$ $\sim U(500, 1000)$ $so_o$ $\sim U(1500, 2500)$ $cap_j$ $\sim U(500, 1000)$ $sd_d$ $\sim U(1500, 2000)$ $\tau_j$ $\sim U(0.3, 0.5)$ $pc_m$ $\sim U(7, 20)$ $q_j$ $\sim U(0.35, 0.6)$ $p_m$ $\sim U(10, 15)$ $\pi_{jkr}$ $\sim U(0.1, 0.5)$ $ope_o$ $\sim U(10, 25)$ $\varepsilon_k$ $\sim U(0.4, 0.6)$ $opd_d$ $\sim U(10, 20)$ $GHs_{sm}$ $\sim U(10, 20)$ $fc_s$ $\sim U(1600, 2200)$ $GHm_{mj}$ $\sim U(10, 20)$ $fU_j$ $\sim U(1600, 2500)$ $GHu_{jk}$ $\sim U(10, 20)$ $fR_j$ $\sim U(1800, 2800)$ $GHr_{jk}$ $\sim U(10, 20)$ $stc_{sm}$ $\sim U(5, 15)$ $GH_{ij}$ $\sim U(10, 20)$ $tc_{mj}$ $\sim U(5, 15)$ $GHk_{kc}$ $\sim U(10, 20)$ $dr_{jk}$ $\sim U(5, 20)$ $GHc_{co}$ $\sim U(10, 20)$ $dp_{jk}$ $\sim U(5, 20)$ $GHd_{cd}$ $\sim U(10, 20)$ $db_{jk}$ $\sim U(5, 20)$ $GHo_{om}$ $\sim U(10, 20)$ $e_{jkr}$ $\sim U(5, 20)$ $A$ $\sim U(100,500)$ $tck_{kc}$ $\sim U(7, 20)$ $pf$ $\sim U(60, 80)$ $tcc_{co}$ $\sim U(8, 20)$
 Parameter Uniform distribution Parameter Uniform distribution $tcd_{cd}$ $\sim U(8, 20)$ $sm_m$ $\sim U(900, 2000)$ $tco_{om}$ $\sim U(10, 20)$ $sc_c$ $\sim U(1500, 2500)$ $pcap_m$ $\sim U(500, 1000)$ $so_o$ $\sim U(1500, 2500)$ $cap_j$ $\sim U(500, 1000)$ $sd_d$ $\sim U(1500, 2000)$ $\tau_j$ $\sim U(0.3, 0.5)$ $pc_m$ $\sim U(7, 20)$ $q_j$ $\sim U(0.35, 0.6)$ $p_m$ $\sim U(10, 15)$ $\pi_{jkr}$ $\sim U(0.1, 0.5)$ $ope_o$ $\sim U(10, 25)$ $\varepsilon_k$ $\sim U(0.4, 0.6)$ $opd_d$ $\sim U(10, 20)$ $GHs_{sm}$ $\sim U(10, 20)$ $fc_s$ $\sim U(1600, 2200)$ $GHm_{mj}$ $\sim U(10, 20)$ $fU_j$ $\sim U(1600, 2500)$ $GHu_{jk}$ $\sim U(10, 20)$ $fR_j$ $\sim U(1800, 2800)$ $GHr_{jk}$ $\sim U(10, 20)$ $stc_{sm}$ $\sim U(5, 15)$ $GH_{ij}$ $\sim U(10, 20)$ $tc_{mj}$ $\sim U(5, 15)$ $GHk_{kc}$ $\sim U(10, 20)$ $dr_{jk}$ $\sim U(5, 20)$ $GHc_{co}$ $\sim U(10, 20)$ $dp_{jk}$ $\sim U(5, 20)$ $GHd_{cd}$ $\sim U(10, 20)$ $db_{jk}$ $\sim U(5, 20)$ $GHo_{om}$ $\sim U(10, 20)$ $e_{jkr}$ $\sim U(5, 20)$ $A$ $\sim U(100,500)$ $tck_{kc}$ $\sim U(7, 20)$ $pf$ $\sim U(60, 80)$ $tcc_{co}$ $\sim U(8, 20)$
Obtained computational results
 Solution No. NSGA-Ⅱ EC Gap (%) Objective 1 Objective 2 Objective 1 Objective 2 1 71014 34028 70924 34000 0.21 2 67542 35047 67467 35000 0.24 3 65195 36039 65133 36000 0.2 4 63167 36424 63105 36389 0.19
 Solution No. NSGA-Ⅱ EC Gap (%) Objective 1 Objective 2 Objective 1 Objective 2 1 71014 34028 70924 34000 0.21 2 67542 35047 67467 35000 0.24 3 65195 36039 65133 36000 0.2 4 63167 36424 63105 36389 0.19
The indices for the sample instances in medium and large-sized
 Indices P1 P2 P3 P4 Suppliers 5 10 20 30 Production centers 5 10 15 25 Distribution centers 5 10 15 30 Customers 8 15 25 40 Collection centers 4 6 10 15 Recovery centers 4 4 15 15 Disposal centers 4 6 10 15
 Indices P1 P2 P3 P4 Suppliers 5 10 20 30 Production centers 5 10 15 25 Distribution centers 5 10 15 30 Customers 8 15 25 40 Collection centers 4 6 10 15 Recovery centers 4 4 15 15 Disposal centers 4 6 10 15
The average value of criteria for the two algorithms at confidence level 0.5
 Criteria DM MID SM NPS Problem Method EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ 1 1.06 1.18 0.88 0.98 1.02 0.96 3 5 2 1.2 1.17 1.1 1.03 1.17 1.03 3 12 3 0.92 0.96 0.92 0.88 0.88 0.76 4 19 4 - 1.12 - 1.45 - 1.39 - 24
 Criteria DM MID SM NPS Problem Method EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ 1 1.06 1.18 0.88 0.98 1.02 0.96 3 5 2 1.2 1.17 1.1 1.03 1.17 1.03 3 12 3 0.92 0.96 0.92 0.88 0.88 0.76 4 19 4 - 1.12 - 1.45 - 1.39 - 24
The average value of criteria for the two algorithms at confidence level 0.7
 Criteria DM MID SM NPS Problem Method EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ 1 1.07 1.14 0.77 0.89 1.35 1.13 2 6 2 0.94 1.08 0.54 0.43 1.79 1.51 4 18 3 1.14 1.26 0.62 0.53 0.96 0.87 2 24 4 - 0.91 - 1.04 - 2.16 - 37
 Criteria DM MID SM NPS Problem Method EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ 1 1.07 1.14 0.77 0.89 1.35 1.13 2 6 2 0.94 1.08 0.54 0.43 1.79 1.51 4 18 3 1.14 1.26 0.62 0.53 0.96 0.87 2 24 4 - 0.91 - 1.04 - 2.16 - 37
The average value of criteria for the two algorithms at confidence level 0.9
 Criteria DM MID SM NPS Problem Method EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ 1 1.137 1.21 0.86 0.74 2.27 2.11 3 7 2 0.98 1.08 1.03 0.92 1.95 1.81 2 13 3 0.83 0.75 0.88 0.93 0.82 0.93 2 18 4 - 1.11 - 1.1.02 - 1.04 - 28
 Criteria DM MID SM NPS Problem Method EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ EC NSGA-Ⅱ 1 1.137 1.21 0.86 0.74 2.27 2.11 3 7 2 0.98 1.08 1.03 0.92 1.95 1.81 2 13 3 0.83 0.75 0.88 0.93 0.82 0.93 2 18 4 - 1.11 - 1.1.02 - 1.04 - 28
The objective functions value for various scenarios
 Scenario Objective 1 Objective 2 Non disruption 58344 34078 Fully disruption 67817 39226 Partial disruption 63105 36389
 Scenario Objective 1 Objective 2 Non disruption 58344 34078 Fully disruption 67817 39226 Partial disruption 63105 36389

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