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

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.