Classifying flexible measures in data envelopment analysis: a slack-based measure

Data envelopment analysis (DEA) has gained a wide range of applications in measuring comparative efficiency of decision making units (DMUs) with multiple incommensurate inputs and outputs. The standard DEA method requires that the status of all input and output variables be known exactly. However, in many real applications, the status of some measures is not clearly known as inputs or outputs. These measures are referred to as flexible measures. This paper proposes a flexible slacks-based measure (FSBM) of efficiency in which each flexible measure can play input role for some DMUs and output role for others to maximize the relative efficiency of the DMU under evaluation. Further, we will show that when an operational unit is efficient in a specific flexible measure, this measure can play both input and output roles for this unit. In this case, the optimal input/output designation for flexible measure is one that optimizes the efficiency of the artificial average unit. An application in assessing UK higher education institutions used to show the applicability of the proposed approach.