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Mathematical Problems in Engineering
Volume 2014, Article ID 702319, 10 pages
http://dx.doi.org/10.1155/2014/702319
Research Article

A Fuzzy Approach Using Generalized Dinkelbach’s Algorithm for Multiobjective Linear Fractional Transportation Problem

1Department of Mathematics, Faculty of Science, Turkish Naval Academy, Tuzla, Istanbul, Turkey
2Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Davutpasa, Istanbul, Turkey

Received 30 September 2013; Revised 14 January 2014; Accepted 21 January 2014; Published 17 March 2014

Academic Editor: Hao-Chun Lu

Copyright © 2014 Nurdan Cetin and Fatma Tiryaki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a multiobjective linear fractional transportation problem (MLFTP) with several fractional criteria, such as, the maximization of the transport profitability like profit/cost or profit/time, and its two properties are source and destination. Our aim is to introduce MLFTP which has not been studied in literature before and to provide a fuzzy approach which obtain a compromise Pareto-optimal solution for this problem. To do this, first, we present a theorem which shows that MLFTP is always solvable. And then, reducing MLFTP to the Zimmermann’s “min” operator model which is the max-min problem, we construct Generalized Dinkelbach’s Algorithm for solving the obtained problem. Furthermore, we provide an illustrative numerical example to explain this fuzzy approach.