A Linear Programming Problem in Fuzzy Space: A Case Study in a Bakery Industry with Managerial Decision A Linear Programming Problem in Fuzzy Space: A Case Study in a Bakery Industry with Managerial Decision

Abstract

This paper investigates 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. 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 a case study application. The proposed procedure was programmed and through MATLAB (R2009a) version software, the four dimensional slice diagram is represented to the application. Finally, real case problem is presented to illustrate the effectiveness of the theoretical results, and to gain additional managerial insights for decision making.