A DEA based Performance Measurement Approach with Weak Ordinal Data

Data Envelopment Analysis (DEA) is a mathematical programming for performance evaluation of a set of similar Decision Making Units (DMUs). In DEA model, it is supposed that the values of inputs and outputs are exactly known. But, in many real world problems these values are imprecise in form of ordinal, bounded data, and so on. Until now, different approaches have been proposed to calculate the relative efficiency in presence of ordinal data in DEA. The focus of this paper is on weak ordinal data. The paper briefly reviews the existing methods in this area and explains some drawbacks of these methods. We show that converting ordinal data to some special exact data and ignoring the DEA axioms lead to these drawbacks. In fact, when data are in ordinal format, there are no observed data, and so the inclusion of observation axiom, the first axiom in DEA, is not established. To overcome the drawbacks and because of the necessity of observation axiom, we propose a new algorithm based on generating n random dataset for the ordinal measures such that the relations among the ordinal data will be satisfied. By considering the inclusion of observation axiom, it will be shown that this algorithm leads to the better result comparing with existing approaches. Several numerical examples are used to explain the content of the paper.