In this paper a supply chain network for producing and distributing the dairy products of a case study is designed. A supply chain with suppliers, potential plants, potential distribution centers, customers, potential collection/recycling centers, potential disposal centers, and multi-mode transportation under cost, environmental, and social based objective functions is formulated mathematically. In the proposed formulation, according to the uncertain nature of the problem in real world situations, some of the parameters are considered as intuitionistic fuzzy values. In addition to the required location and allocation decisions, two main difficulties of the proposed problem are its uncertain nature and its multi-objectivity. To overcome such difficulties, a method considering the acceptance degree of fuzzy constraints violated is used to convert the fuzzy formulation to its equivalent crisp form. As a novelty, this method for the first time is modified for intuitionistic fuzzy values. Then the obtained multi-objective crisp formulation is solved by five multi-objective optimization approaches of the literature. At the end the data of the case study from Iran is used to evaluate the proposed crisp formulation and comparison of the multi-objective solution approaches.
