A fuzzy mathematical multi-period multi-echelon supply chain model based on extension principle

This paper deals with multi-echelon integrated purchase, production and distribution planning model in a supply chain system. The manufacturer procures raw material from suppliers then proceed to convert it as finished product, and finally delivers to the distribution centers in order to minimize the total cost of the chain, which faces imprecise and ill-known data, called fuzzy supply, process and demand of customers. The model has been formulated as a fuzzy linear programming model. Here, the triangular fuzzy numbers are considered because the triangular form is the simplest type of fuzzy numbers and gives the most important information about a fuzzy number. The main objective of this paper is to solve fuzzy linear programming problems more efficiently. In order to secularize the fuzzy linear programming model, an evaluation method is used wherein the proposed approach enables the decision maker to obtain alternative decision plans with different degrees of satisfaction. A noteworthy feature of this approach is that it is able to find the membership function of the fuzzy objective value and decision variables which is derived numerically by enumerating different values of a-cuts of the fuzzy triangular number. Finally, a numerical example is presented to clarify the features of the proposed approach.