Lower Bound Restrictions on Intensities in Data Envelopment Analysis

Abstract

We propose an extension to the basic DEA models that guarantees that if an intensity is positive then it must be at least as large as a pre-defined lower bound. This requirement adds an integer programming constraint known within Operations Research as a Fixed-Charge (FC) type of constraint. Accordingly, we term the new model DEA_FC. The proposed model lies between the DEA models that allow units to be scaled arbitrarily low, and the Free Disposal Hull model that allows no scaling. We analyze 18 datasets from the literature to demonstrate that sufficiently low intensities—those for which the scaled Decision-Making Unit (DMU) has inputs and outputs that lie below the minimum values observed—are pervasive, and that the new model ensures fairer comparisons without sacrificing the required discriminating power. We explain why the “low-intensity” phenomenon exists. In sharp contrast to standard DEA models we demonstrate via examples that an inefficient DMU may play a pivotal role in determining the technology. We also propose a goal programming model that determines how deviations from the lower bounds affect efficiency, which we term the trade-off between the deviation gap and the efficiency gap.