Efficiency analysis of non-homogeneous parallel sub-unit systems for the performance measurement of higher education

Conventional Data Envelopment Analysis (DEA) models focus only on initial inputs and final outputs for efficiency evaluation. Thus, these models treat the production process as a ‘black box’, i.e., they do not take into account how exactly inputs are related to outputs. Various models that came later take care of internal processes of DMU. The existing models of internal processes for parallel sub-units consist of three stages: the first stage calculates the relative weights of sub-units, the second stage calculates the efficiencies of sub-units, and in the third stage efficiencies of sub-units are aggregated as the efficiency of DMU. It is observed that when existing models of internal processes are applied to non-homogeneous parallel sub-units, in the first stage, the weight assigned to the maximum efficient sub-unit is one and to other sub-units is zero. This implies that the efficiency of a DMU is equal to the maximum of efficiencies of its sub-units indicating that the efficiency of a DMU is not sensitive to the efficiencies of sub-units other than the sub-unit with maximum efficiency. This paper proposes a single stage DEA approach where the efficiency of a DMU and its sub-units can be measured simultaneously. The advantage of the proposed approach is that the efficiency of a DMU is sensitive to the changes in the efficiency of its sub-units, and weights of sub-units can be assigned a priori by the decision maker. The development of the proposed approach is inspired from the growing interest in evaluating efficiency of higher education system in India. In the proposed application, states are considered as DMUs and universities, colleges and stand-alone institutions are taken as three non-homogeneous parallel sub-units of DMUs.