A Two-Fold Linear Programming Model with Fuzzy Data

Linear programming (LP) is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency. Although LP models require well-suited information and precise data, managers and decision makers dealing with optimization problems often have a lack of information on the exact values of some parameters used in their models. Fuzzy sets provide a powerful tool for dealing with this kind of imprecise, vague, uncertain or incomplete data. In this paper, we propose a two-fold model which consists of two new methods for solving fuzzy LP (FLP) problems in which the variables and the coefficients of the constraints are characterized by fuzzy numbers. In the first method, we transform our FLP model into a conventional LP model by using a new fuzzy ranking method and introducing a new supplementary variable to obtain the fuzzy and crisp optimal solutions simultaneously with a single LP model. In the second method, we propose a LP model with crisp variables for identifying the crisp optimal solutions. We demonstrate the details of the proposed method with two numerical examples