DEA models for non-homogeneous DMUs with different input configurations

The data envelopment analysis (DEA) methodology is a benchmarking tool where it is generally assumed that decision making units (DMUs) constitute a homogeneous set; specifically, it is assumed that all DMUs have a common (input, output) bundle. In earlier work by the authors the issue of non-homogeneity on the output side was investigated. There we examined a set of steel fabrication plants where not all plants produced the same set of products/outputs. In the current research we investigate non-homogeneity on the input side. Such can occur in manufacturing plants, for example, when the output bundle can be produced using different mixes of machines, robots and laborers. Thus, we can have an input configuration existing in a DMU that is different from the configuration in another DMU. As a practical application of this phenomenon, we examine the measurement of efficiencies of a set of provinces in China. There, all provinces have the same common set of outputs in the form of GDP, supported population, and an undesirable output, nitrogen dioxide. On the input side, however, this commonality is missing. While all provinces have water, capital investment and natural resources, the latter of these (natural resources) takes several different forms, namely coal, natural gas and petroleum. However, not all provinces have the same mix of these resources, nor are there clear exchange rates among these very different, albeit substitutable inputs. This means that that one cannot directly apply the conventional DEA methodology. This then raises the question as to how to fairly evaluate efficiency when the configuration or mix of inputs can differ from one DMU to another. To address this, we view the generation of outputs for a province as a set of processes created by the different configurations of natural resources available. We develop a DEA type of methodology to evaluate these processes. This evaluation provides important insights into not only the overall performance of each province, but as well provides measures of the efficiency of the various configurations of the three natural resources. © 2016 Elsevier B.V. All rights reserved.