Efficiency evaluation of non-homogeneous DMUs with inconsistent input quality

Abstract

This paper focuses on a heterogeneity issue that the quality of inputs fluctuates across decision making units (DMUs), and proposes a data envelopment analysis (DEA) based methodology to evaluate the efficiencies of DMUs involved in this issue. The evaluation proceeds in two steps. Firstly, the quality of an input is considered as the overall perception of the influence its various attributes exert on production, then the linear relation and exponential relation are assumed respectively in expressing input quality by aggregating its attribute indicators. Based on the two expressions of input quality, two corresponding models are developed for efficiency measure, in the second step. In the models, the quality difference of an input in DMUs is reflected by its weights. A weight restriction is incorporated into models, and ensures that the magnitudes of an input’s weights in DMUs remain the same order with its quality. Our developed method makes the evaluation reasonable and acceptable, thereby enhancing the usefulness of DEA. The example of the 2012 London Olympics is employed to illustrate the methodology.