Optimal solution of pentagonal fuzzy transportation problem using a new ranking technique

Abstract

In this article, we propose a method based on a new ranking technique to find optimal solution for a pentagonal fuzzy transportation problem. Firstly, the proposed ranking method which is based on the centroid concept is applied. This transforms the pentagonal fuzzy transportation problem to crisp transportation problem and then the proposed algorithm is applied to find optimal solution of the problem in crisp form. Also, a new method to find initial basic feasible solution (IBFS) of crisp valued transportation problems is introduced in the paper. Further, we give two numerical illustrations for the newly proposed algorithm and compare the solution obtained with the solutions of existing methods. The proposed method can easily be understood and applied to real life transportation problems. Moreover, the proposed ranking method can be used to solve various other fuzzy problems of operations research.

Keywords

• fuzzy transportation problem
• fuzzy number
• pentagonal fuzzy number
• ranking function
• optimal solution