Document Type : Original Article


1 Ph.D. Student, Allameh Tabataba'i University.

2 Professor, Allameh Tabatabaei University.

3 Professor, Allameh Tabataba'i University.

4 Associate Professor, Iran University of Science and Technology.


Considering the cognitive, random, uncertain, and flexible constraints, a robust, stochastic, possibilistic, and flexible chance-constrained model was developed based on credibility measurement. The ultimate aim was closed-loop supply chain network design. Different attitudes of decision-makers were answered by more flexible measurements of optimistic and pessimistic parameters in the form of credibility measurement. The model has been able to reduce the possible deviation, stochastic deviations, non-fulfillment of demand and capacity constraints, and violation of flexible constraints, which simultaneously include cognitive and random uncertainties and flexibility of constraints in the model. To apply the model, a case study was conducted to design the closed-loop supply chain network of multi-product and multi-period stone paper. The results of implementing the model showed that in different situations and according to the importance of decision makers' opinions, using the range of optimism and pessimism, the number, location of facilities, optimal flow of products and materials between centers in the stone paper supply chain network can be determined. The proposed model was evaluated using robustness and sensitivity analysis, and its performance was evaluated using nominal data in the realization model, which results showed the appropriate performance of the model.


Main Subjects

  1. Amiri, M., Hosseini Dehshiri, S. J., & Yousefi Hanoomarvar, A. (2018). Determining the Optimal Combination of Larg Supply Chain Strategies Using SWOT Analysis, Multi-criteria Decision-making Techniques and Game Theory. Industrial Management Journal10(2), 221-246. (In Persian)
  2. Atabaki, M. S., Mohammadi, M., & Naderi, B. (2020). New robust optimization models for closed-loop supply chain of durable products: Towards a circular economy. Computers & Industrial Engineering, 146, 106520.
  3. Baghalian, A., Rezapour, S., & Farahani, R. Z. (2013). Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case. European Journal of Operational Research, 227(1), 199-215.
  4. Boronoos, M., Mousazadeh, M., & Torabi, S. A. (2020). A robust mixed flexible-possibilistic programming approach for multi-objective closed-loop green supply chain network design. Environment, Development and Sustainability, 23(3), 3368-3395. doi:10.1007/s10668-020-00723-z
  5. Carlsson, C., & Fullér, R. (2001). On possibilistic mean value and variance of fuzzy numbers. Fuzzy sets and systems, 122(2), 315-326.
  6. Dahooie, J. H., Dehshiri, S. J. H., Banaitis, A., & Binkytė-Vėlienė, A. (2020). Identifying and prioritizing cost reduction solutions in the supply chain by integrating value engineering and gray multi-criteria decision-making. Technological and Economic Development of Economy26(6), 1311-1338.
  7. Dehghan, E., Nikabadi, M. S., Amiri, M., & Jabbarzadeh, A. (2018). Hybrid robust, stochastic and possibilistic programming for closed-loop supply chain network design. Computers & Industrial Engineering, 123, 220-231.
  8. Farrokh, M., Azar, A., Jandaghi, G., & Ahmadi, E. (2018). A novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty. Fuzzy sets and systems, 341, 69-91.
  9. Fazli-Khalaf, M., Khalilpourazari, S., & Mohammadi, M. (2019). Mixed robust possibilistic flexible chance constraint optimization model for emergency blood supply chain network design. Annals of operations research, 283(1), 1079-1109.
  10. Ghahremani-Nahr, J., Kian, R., & Sabet, E. (2019). A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm. Expert systems with applications, 116, 454-471.
  11. Gilani, H., & Sahebi, H. (2021). Optimal Design and Operation of the green pistachio supply network: A robust possibilistic programming model. Journal of Cleaner Production, 282, 125212.
  12. Govindan, K., & Soleimani, H. (2017). A review of reverse logistics and closed-loop supply chains: a Journal of Cleaner Production focus. Journal of Cleaner Production, 142, 371-384.
  13. Guide Jr, V. D. R., & Van Wassenhove, L. N. (2009). OR FORUM—The evolution of closed-loop supply chain research. Operations research, 57(1), 10-18.
  14. Günay, E. E., Kremer, G. E. O., & Zarindast, A. (2020). A multi-objective robust possibilistic programming approach to sustainable public transportation network design. Fuzzy sets and systems.
  15. Hatefi, S. M., & Jolai, F. (2014). Robust and reliable forward–reverse logistics network design under demand uncertainty and facility disruptions. Applied Mathematical Modelling, 38(9-10), 2630-2647.
  16. Heidary Dahooie, J., Hosseini Dehshiri, S. (2019). Identify and prioritize Strategies to Reduce Plant Power Equipments Supply Chain Costs Through Value Engineering. Industrial Management Studies, 17(52), 125-152. (In Persian)
  17. Hosseini Dehshiri, S., Heydari Dehooei.Zohrabi, J. (2019). Using Gray Numbers Theory in Multi-Attribute Decision Making Methods for the Evaluation the Risk of Outsourcing of Information Technology Projects. IT Management Studies, 7(28), 167-198. (In Persian)
  18. Hosseini-Motlagh, S.-M., Samani, M. R. G., & Cheraghi, S. (2020). Robust and stable flexible blood supply chain network design under motivational initiatives. Socio-economic planning sciences, 70, 100725.
  19. Inuiguchi, M., & Ramı́k, J. (2000). Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy sets and systems, 111(1), 3-28.
  20. Jabbarzadeh, A., Haughton, M., & Khosrojerdi, A. (2018). Closed-loop supply chain network design under disruption risks: A robust approach with real world application. Computers & Industrial Engineering, 116, 178-191.
  21. Jafarnejad, A., Mohseni, M., Abdollahi, A. (2014). Proposing a Hybrid Fuzzy PROMETHEE - AHP Approach to Performance Evaluation of Service Supply Chain (Case Study: Hotel industry). Journal of Industrial Management Perspective, 4(Issue 2), 69-92. (In Persian)
  22. Kouchaki Tajani, T., Mohtashami, A., Amiri, M., Ehtesham Rasi, R. (2021). Presenting a Robust Optimization Model to Design a Comprehensive Blood Supply Chain under Supply and Demand Uncertainties. Journal of Industrial Management Perspective, 11(Issue 1), 81-116. (In Persian)
  23. Liao, H., Deng, Q., Wang, Y., Guo, S., & Ren, Q. (2018). An environmental benefits and costs assessment model for remanufacturing process under quality uncertainty. Journal of Cleaner Production, 178, 45-58.
  24. Liu, B., & Liu, Y.-K. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE transactions on Fuzzy Systems, 10(4), 445-450.
  25. Liu, Y., Ma, L., & Liu, Y. (2021). A novel robust fuzzy mean-UPM model for green closed-loop supply chain network design under distribution ambiguity. Applied Mathematical Modelling, 92, 99-135.
  26. Mousazadeh, M., Torabi, S. A., & Pishvaee, M. S. (2014). Green and reverse logistics management under fuzziness. In Supply chain management under fuzziness (pp. 607-637): Springer.
  27. Mousazadeh, M., Torabi, S. A., & Zahiri, B. (2015). A robust possibilistic programming approach for pharmaceutical supply chain network design. Computers & Chemical Engineering, 82, 115-128.
  28. Mousazadeh, M., Torabi, S. A., Pishvaee, M., & Abolhassani, F. (2018). Accessible, stable, and equitable health service network redesign: A robust mixed possibilistic-flexible approach. Transportation Research Part E: Logistics and Transportation Review, 111, 113-129.
  29. Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large-scale systems. Operations research, 43(2), 264-281.
  30. Peidro, D., Mula, J., Poler, R., & Verdegay, J.-L. (2009). Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. Fuzzy sets and systems, 160(18), 2640-2657.
  31. Pishvaee, M. S., & Khalaf, M. F. (2016). Novel robust fuzzy mathematical programming methods. Applied Mathematical Modelling, 40(1), 407-418.
  32. Pishvaee, M. S., & Torabi, S. A. (2010). A possibilistic programming approach for closed-loop supply chain network design under uncertainty. Fuzzy sets and systems, 161(20), 2668-2683.
  33. Pishvaee, M. S., Farahani, R. Z., & Dullaert, W. (2010). A memetic algorithm for bi-objective integrated forward/reverse logistics network design. Computers & Operations Research, 37(6), 1100-1112.
  34. Pishvaee, M. S., Rabbani, M., & Torabi, S. A. (2011). A robust optimization approach to closed-loop supply chain network design under uncertainty. Applied Mathematical Modelling, 35(2), 637-649.
  35. Pishvaee, M. S., Razmi, J., & Torabi, S. A. (2012). Robust possibilistic programming for socially responsible supply chain network design: A new approach. Fuzzy sets and systems, 206, 1-20.
  36. Tabrizi, B. H., & Razmi, J. (2013). Introducing a mixed-integer non-linear fuzzy model for risk management in designing supply chain networks. Journal of Manufacturing Systems, 32(2), 295-307.
  37. Talaei, M., Moghaddam, B. F., Pishvaee, M. S., Bozorgi-Amiri, A., & Gholamnejad, S. (2016). A robust fuzzy optimization model for carbon-efficient closed-loop supply chain network design problem: a numerical illustration in electronics industry. Journal of Cleaner Production, 113, 662-673.
  38. Torabi, S., Namdar, J., Hatefi, S., & Jolai, F. (2016). An enhanced possibilistic programming approach for reliable closed-loop supply chain network design. International Journal of Production Research, 54(5), 1358-1387.
  39. Tsao, Y.-C., & Thanh, V.-V. (2019). A multi-objective mixed robust possibilistic flexible programming approach for sustainable seaport-dry port network design under an uncertain environment. Transportation Research Part E: Logistics and Transportation Review, 124, 13-39.
  40. Xu, J., & Zhou, X. (2013). Approximation based fuzzy multi-objective models with expected objectives and chance constraints: Application to earth-rock work allocation. Information Sciences, 238, 75-95.
  41. Yadegari, E., Alem-Tabriz, A., & Zandieh, M. (2019). A memetic algorithm with a novel neighborhood search and modified solution representation for closed-loop supply chain network design. Computers & Industrial Engineering, 128, 418-436.
  42. Yaghin, R. G., Sarlak, P., & Ghareaghaji, A. (2020). Robust master planning of a socially responsible supply chain under fuzzy-stochastic uncertainty (A case study of clothing industry). Engineering Applications of Artificial Intelligence, 94, 103715.
  43. Yavari, M., & Geraeli, M. (2019). Heuristic method for robust optimization model for green closed-loop supply chain network design of perishable goods. Journal of Cleaner Production, 226, 282-305.
  44. Yu, C.-S., & Li, H.-L. (2000). A robust optimization model for stochastic logistic problems. International Journal of Production Economics, 64(1-3), 385-397.
  45. Yu, L., & Li, Y. (2019). A flexible-possibilistic stochastic programming method for planning municipal-scale energy system through introducing renewable energies and electric vehicles. Journal of Cleaner Production, 207, 772-787.
  46. Zarrinpoor, N., & Omidvari, Z. (2020). A Robust Optimization Model for the Strategic and Operational Design of the Oil Supply Chain. Journal of Industrial Management Perspective, 10(Issue 4), 155-191. (In Persian)
  47. Zhang, P., & Zhang, W.-G. (2014). Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints. Fuzzy sets and systems, 255, 74-91.
  48. Zhang, W.-G., & Xiao, W.-L. (2009). On weighted lower and upper possibilistic means and variances of fuzzy numbers and its application in decision. Knowledge and information systems, 18(3), 311-330.‌