Solving a supply chain problem using two approaches of fuzzy goal programming based on TOPSIS and fuzzy preference relations

Document Type : Research Paper


Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran


Supply chain problems have many ambiguous parameters, and decisions about these types of problems, which are usually multi-objective, should be made according to the constraints and priorities of the objectives. In this paper, we will examine the integrated model of supply chain network with supply, production and distribution levels, considering the logistics costs and service level simultaneously under uncertainty. In multi-objective Mixed Integer Linear Programming (MILP) model, objectives are considered as fuzzy and with different priorities and to eliminate the ambiguity in membership values of fuzzy objectives, priorities are adjusted with fuzzy relations. The model is solved by two approaches of Fuzzy Goal Programming (FGP) and their results are compared. Presenting a multi-period multi-level multi-product multi-objective model in the field of designing and distribution of supply chains and presenting two methods of fuzzy goal programming and the results are compared to provide a suitable method to convert the proposed model into a fuzzy model are the contributions of this paper. The computational results show that the first method in the criterion of cumulative weight of fuzzy membership values ​​and the second method in determining the cumulative weight of ambiguous preferences of decision-maker have had a good performance. The results of ANOVA and Mann-Whitney tests, show that  of all three criteria is less than acceptable level (0.05) and e first method had a good performance in determining the criterion of membership value of cumulative weight of fuzzy objectives.


Main Subjects

Aköz, O., & Petrovic, D. (2007). A fuzzy goal programming method with imprecise goal hierarchy. European journal of operational research181(3), 1427-1433.
Babaee Tirkolaee, E., Hadian, S., & Golpira, H. (2019). A novel multi-objective model for two-echelon green routing problem of perishable products with intermediate depots. Journal of Industrial Engineering and Management Studies6(2), 101-110.
Caramia, M., & Dell’Olmo, P. (2020). Multi-objective optimization. In Multi-objective management in freight logistics (pp. 21-51). Springer, Cham.
Chakraborty, D., Guha, D., & Dutta, B. (2016). Multi-objective optimization problem under fuzzy rule constraints using particle swarm optimization. Soft Computing, 20(6), 2245-2259.
Colapinto, C., Jayaraman, R., & La Torre, D. (2020). Goal programming models for managerial strategic decision making. In Applied Mathematical Analysis: Theory, Methods, and Applications (pp. 487-507). Springer, Cham.
Dalman, H. (2016). An interactive fuzzy goal programming algorithm to solve decentralized bi-level multiobjective fractional programming problem. arXiv preprint arXiv:1606.00927.
Fahimnia, B., & Jabbarzadeh, A. (2016). Marrying supply chain sustainability and resilience: A match made in heaven. Transportation Research Part E: Logistics and Transportation Review91, 306-324.
Ghasemi, P., Khalili-Damghani, K., Hafezalkotob, A., & Raissi, S. (2019a). Stochastic optimization model for distribution and evacuation planning (A case study of Tehran earthquake). Socio-Economic Planning Sciences, 100745.
Ghasemi, P., Khalili-Damghani, K., Hafezalkotob, A., & Raissi, S. (2019b). Uncertain multi-objective multi-commodity multi-period multi-vehicle location-allocation model for earthquake evacuation planning. Applied Mathematics and Computation350, 105-132.
Ghasemi, P., Khalili-Damghani, K., Hafezolkotob, A., & Raissi, S. (2017). A decentralized supply chain planning model: a case study of hardboard industry. The International Journal of Advanced Manufacturing Technology93(9-12), 3813-3836.
Giri, P. K., Maiti, M. K., & Maiti, M. (2014). Fuzzy stochastic solid transportation problem using fuzzy goal programming approach. Computers & Industrial Engineering72, 160-168.
Hanks, R. W., Lunday, B. J., & Weir, J. D. (2020). Robust goal programming for multi-objective optimization of data-driven problems: A use case for the United States transportation command's liner rate setting problem. Omega90, 101983.
Hardy, C., Bhakoo, V., & Maguire, S. (2020). A new methodology for supply chain management: Discourse analysis and its potential for theoretical advancement. Journal of Supply Chain Management56(2), 19-35.
Hocine, A., Zhuang, Z. Y., Kouaissah, N., & Li, D. C. (2020). Weighted-additive fuzzy multi-choice goal programming (WA-FMCGP) for supporting renewable energy site selection decisions. European Journal of Operational Research.
Khalili-Damghani, K., & Ghasemi, P. (2016). Uncertain Centralized/Decentralized Production-Distribution Planning Problem in Multi-Product Supply Chains: Fuzzy Mathematical Optimization Approaches. Industrial Engineering & Management Systems15(2), 156-172.
Khalili-Damghani, K., & Sadi-Nezhad, S. (2013). A decision support system for fuzzy multi-objective multi-period sustainable project selection. Computers & Industrial Engineering64(4), 1045-1060.
Khalili-Damghani, K., & Shahrokh, A. (2014). Solving a new multi-period multi-objective multi-product aggregate production planning problem using fuzzy goal programming. Industrial Engineering & Management Systems13(4), 369-382.
Khalili-Damghani, K., Sadi-Nezhad, S., & Tavana, M. (2013). Solving multi-period project selection problems with fuzzy goal programming based on TOPSIS and a fuzzy preference relation. Information Sciences, 252, 42-61.

Khan, M. F., Hasan, M., Quddoos, A., Fügenschuh, A., & Hasan, S. S. (2020). Goal Programming Models with Linear and Exponential Fuzzy Preference Relations. Symmetry, 12(6), 934.
Kilic, H. S., & Yalcin, A. S. (2020). Modified two-phase fuzzy goal programming integrated with IF-TOPSIS for green supplier selection. Applied Soft Computing, 106371.
Ku, C. Y., Chang, C. T., & Ho, H. P. (2010). Global supplier selection using fuzzy analytic hierarchy process and fuzzy goal programming. Quality & Quantity44(4), 623-640.
Kumar, L., Jain, P. K., & Sharma, A. K. (2020). A fuzzy goal programme–based sustainable Greenfield supply network design for tyre retreading industry. The International Journal of Advanced Manufacturing Technology, 1-26.
Loetamonphong, J., Fang, S. C., & Young, R. E. (2002). Multi-objective optimization problems with fuzzy relation equation constraints. Fuzzy Sets and Systems, 127(2), 141-164.
Majumder, D., Bhattacharjee, R., & Dam, M. (2020). Fuzzy Supply Chain Performance Measurement Model Based on SCOR 12.0. In Intelligent Computing in Engineering (pp. 1129-1139). Springer, Singapore.
Mohtashami, A., Alinezhad, A., & Niknamfar, A. H. (2020). A fuzzy multi-objective model for a cellular manufacturing system with layout designing in a dynamic condition. International Journal of Industrial and Systems Engineering34(4), 514-543.
Nomani, M. A., Ali, I., Fügenschuh, A., & Ahmed, A. (2017). A fuzzy goal programming approach to analyse sustainable development goals of India. Applied Economics Letters24(7), 443-447.
Pal, B. B., Porchelvi, R. S., & Biswas, A. (2017). Chance-Constrained Fuzzy Goal Programming with Penalty Functions for Academic Resource Planning in University Management Using Genetic Algorithm. In Nature-Inspired Computing and Optimization (pp. 449-474). Springer, Cham.
Rabbani, M., Mamaghani, M. G., Farshbaf-Geranmayeh, A., & Mirzayi, M. (2016). A novel mixed integer programming formulation for selecting the best renewable energies to invest: A fuzzy goal programming approach. International Journal of Operations Research and Information Systems (IJORIS)7(3), 1-22.
Razmi, J., Jafarian, E., & Amin, S. H. (2016). An intuitionistic fuzzy goal programming approach for finding pareto-optimal solutions to multi-objective programming problems. Expert Systems with Applications65, 181-193.
Subulan, K., Taşan, A. S., & Baykasoğlu, A. (2015). Designing an environmentally conscious tire closed-loop supply chain network with multiple recovery options using interactive fuzzy goal programming. Applied Mathematical Modelling39(9), 2661-2702.
Tirkolaee, E. B., Goli, A., & Weber, G. W. (2020a). Fuzzy Mathematical Programming and Self-Adaptive Artificial Fish Swarm Algorithm for Just-in-Time Energy-Aware Flow Shop Scheduling Problem with Outsourcing Option. IEEE Transactions on Fuzzy Systems.
Tirkolaee, E. B., Mardani, A., Dashtian, Z., Soltani, M., & Weber, G. W. (2020b). A novel hybrid method using fuzzy decision making and multi-objective programming for sustainable-reliable supplier selection in two-echelon supply chain design. Journal of Cleaner Production250, 119517.
Zandkarimkhani, S., Mina, H., Biuki, M., & Govindan, K. (2020). A chance constrained fuzzy goal programming approach for perishable pharmaceutical supply chain network design. Annals of Operations Research, 1-28.