Measuring efficiency in DEA in the presence of common inputs

Data envelopment analysis (DEA) is a methodology for evaluating the relative efficiencies of a set of decision-making units (DMUs). It is commonly assumed that the DMUs are independent of one another, in that each has its own quantities of a set of inputs and outputs. In case this assumption of independence of DMUs holds, decreasing the inputs of one DMU will not affect the inputs of others. The current paper moves beyond the conventional framework and examines a problem setting where there is an interdependence among the DMUs. Consider the case where the members of a given subgroup of DMUs have an input in common, such as would be the case if a set of highway maintenance crews in a district are under the jurisdiction of a district supervisor and district-level resources. The efficiency measurement difficulty created by this “shared’ resource phenomenon is that in attempting to move an inefficient crew towards the frontier by reducing that shared resource (hence penalising that crew), the other crews in that same district will be equally penalised. Specifically, decreasing district resources in relation to their impact on a maintenance crew will cause that resource to decrease as well for other members of the same group. The conventional (input-oriented) DEA model that does not cater for such interdependence situations will fail to address this important issue. To capture this interdependence, we develop a new DEA-like methodology. One of the properties of this new methodology is that its production possibility set cannot be defined in the same manner as in the conventional DEA setting. This is due to the fact that when the DMU under evaluation is projected towards the frontier, the input/output structures of the other units in the same group are altered, unlike the conventional situation where the structures of the other DMUs remain fixed. We apply this new methodology to the problem of evaluating a set of departments in a university setting, where the departments are grouped under various faculties.