Fuzzy DEA Approach for Solving Extended Fuzzy Transportation Problem Based Upon Fuzzy Arithmetic

The central concept in transportation problem (TP) is to determine the minimum total transportation cost or maximum total transportation profit of a commodity for satisfying the demand at destinations using the available supply at the origins. The existing TPs are limited to consideration unit of shipping cost or profit along an arc. However, in many real applications, various inputs and outputs are considered in a TP. Hence, a data envelopment analysis (DEA) based approach has been proposed in the literature when the decision maker has several different goals to achieve for each possible shipment. This paper extends the existing approach to fuzzy environments to account for real situations where input–output data includes uncertainty of triangular membership form. A fuzzy DEA model constructed from the perspective of fuzzy arithmetic is proposed to deal with fuzziness in input and output data. The concept of fuzzy relative efficiency is defined for each possible transportation plan and a transportation plan with maximum fuzzy efficiency is selected as an efficient fuzzy plan.

Transportation Problem, Data Envelopment Analysis, Fuzzy Arithmetic, Fuzzy Efficiency.