Data Envelopment Analysis with Nonhomogeneous DMUs

Data envelopment analysis (DEA), as originally proposed, is a methodology for evaluating the relative efficiencies of a set of homogeneous decision-making units (DMUs) in the sense that each uses the same input and output measures (in varying amounts from one DMU to another). In some situations, however, the assumption of homogeneity among DMUs may not apply. As an example, consider the case where the DMUs are plants in the same industry that may not all produce the same products. Evaluating efficiencies in the absence of homogeneity gives rise to the issue of how to fairly compare a DMU to other units, some of which may not be exactly in the same “business.” A related problem, and one that has been examined extensively in the literature, is the missing data problem; a DMU produces a certain output, but its value is not known. One approach taken to address this problem is to “create” a value for the missing output (e.g., substituting zero, or by taking the average of known values), and use it to fill in the gaps. In the present setting, however, the issue isn’t that the data for the output is missing for certain DMUs, but rather that the output isn’t produced. We argue herein that if a DMU has chosen not to produce a certain output, or for any reason cannot produce that output, and therefore does not put the resources in place to do so, then it would be inappropriate to artificially assign that DMU a zero value or some “average” value for the nonexistent factor. Specifically, the desire is to fairly evaluate a DMU for what it does, rather than penalize or credit it for what it doesn’t do. In the current paper we present DEA-based models for evaluating the relative efficiencies of a set of DMUs where the requirement of homogeneity is relaxed. We then use these models to examine the efficiencies of a set of manufacturing plants.