A fuzzy linear programming approach to mix product selection problem

In this paper, we consider linear programming problems with fuzzy objective function coefficients. In this case, the optimal solution set is defined as a fuzzy set. A new method to find the most significant solutions of the fuzzy problem, together with their importance degrees, has been developed. The new method works directly on the main LP problem by readapting the simplex algorithm to fuzzy arithmetic and using a proper fuzzy ranking criterion. The main advantages, compared with the state-of-the-art, consist in solving the original (fuzzy) LP problem, rather than a set of simplified versions, and generating a list of the most relevant solutions with their importance degree, instead of a set of solutions obtained with different defuzzification methods. A literature case study of mix product selection problem is analyzed as benchmark.