Production possibility of production plans in DEA with imprecise input and output

Abstract

Data Envelopment Analysis (DEA) is a mathematical approach to evaluate the relative efficiency of Decision Making Units (DMUs). DEA models create an efficient frontier using the best observed data. This frontier bounds all feasible production plans named Production Possibility Set. Traditional DEA models require crisp input and output data, but in many situations the data are not precisely available. When the data of the DMUs are imprecise, the location of the efficient frontier cannot be determined precisely therefore the boundary of the production possibility set is imprecise. This paper assumes that some of the data are in the interval format available and then considers the production possibility set as a fuzzy set that all the production plans belong to this set with different degrees of membership and a membership function for the production plans related to the fuzzy production possibility set is derived under a geometrical approach. © Maxwell Scientific Organization, 2013.