Lower bound restrictions on intensities in data envelopment analysis

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 lo wer bound. This requirement adds an integer programming constraint known wi thin Operations Research as a Fixed-Charge (FC) type of constraint. Accordi ngly, 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 Disposa l Hull model that allows no scaling. We analyze 18 datasets from the litera ture to demonstrate that sufficiently low intensities-those for which the s caled Decision-Making Unit (DMU) has inputs and outputs that lie below the minimum values observed-are pervasive, and that the new model ensures faire r comparisons without sacrificing the required discriminating power. We exp lain why the "low-intensity" phenomenon exists. In sharp contrast to standa rd DEA models we demonstrate via examples that an inefficient DMU may play a pivotal role in determining the technology. We also propose a goal progra mming model that determines how deviations from the lower bounds affect eff iciency, which we term the trade-off between the deviation gap and the effi ciency gap.