Managerial decision mechanism to fuzzy optimal solutions in linear programming problems and post-optimal analyses: robust ranking technique

Abstract

In this paper, I wish to find the solutions to the fuzzy linear program where some parameters are fuzzy numbers. 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, a very effective method is introduced for solving these problems. The model is illustrated with application and a sensitivity analysis is obtained. This paper extends linear programming-based problem in fuzzy environment. 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 ranking technique. The proposed procedure was programmed and through MATLAB (R2009a) version software, the four dimensional slice diagram is represented to the application. The model is illustrated with an application and a post optimal analysis is studied with respect to changes in parameter which incorporates all concepts of a fuzzy arithmetic approach to draw managerial insights.