This paper surveys recent techniques that have been developed for optimization of linear programming problems. In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either probabilistic programming or multi objective programming methods. Unfortunately all these methods have shortcomings. In this note, using the concept of comparison of fuzzy numbers, it is introduced a very effective method for solving these problems. This paper extends by applying Big-M method in fuzzy based linear programming problems to obtain optimal solutions. With the problem assumptions, the optimal solution can still be theoretically solved using the simplex based method. To handle the fuzzy decision variables can be initially generated and then solved and improved sequentially using the fuzzy decision approach by introducing Robust’s ranking technique. The model is illustrated with application and the post optimal analyses approaches are obtained. The proposed procedure was programmed and through MATLAB (R2009a) version software, the four dimensional slice diagram is represented to the application. Finally, numerical example is presented to illustrate the effectiveness of the theoretical results, and to gain additional managerial insights for decision making.

Fuzzy, Trapezoidal Number, Linear Programming, Big-M Method, Post Optimal Analyses