Data envelopment analysis with discrete-valued inputs and outputs

The conventional data envelopment analysis (DEA) measures the relative efficiencies of a set of decision making units, which has real‐valued inputs and outputs. In many real occasions, there are cases in which some inputs and/or outputs must only take some particularised real or integer values. These values are referred to as discrete data. The need to deal with discrete‐valued data in DEA naturally occurs when we use real‐valued or integer‐valued DEA, but the reduced inputs and outputs of an inefficient decision making unit are restricted to some particular real or integer values. In this case, axioms such as unbounded ray, convexity and free disposability as discussed in the conventional DEA are violated. In this paper, an alternative extension of DEA in the case of discrete‐valued data has been faced. An axiomatic foundation is proposed to define the new production possibility set. In order to exemplify the method, a case of 25 Iranian gas companies' activities are illustrated.