Limiting flexibility in nonparametric efficiency evaluations: An ex post k-centroid clustering approach

An attractive feature of standard data envelopment analysis (DEA) is that decision-making units (DMUs) are put in their best possible light. This is accomplished by not imposing any restrictions on how the inputs and outputs can be weighted together. Unfortunately, this flexibility also has drawbacks. The underlying best practice production structure is typically very complex, which can make it difficult to understand efficiency evaluations. This flexibility may also motivate DMUs to pick specialized input‒output combinations simply to appear more efficient, particularly in applications where they are rewarded based on their DEA performance. In this paper, we therefore propose an approach that retains the fundamental principles of DEA while reducing flexibility in the evaluations. Our approach entails performing ex post k-centroid clustering of DMUs according to their input‒output mix patterns. The resulting mixed-integer programming problem seeks to put the centroids (as prototypes of their generated clusters) in their best possible light. This clustering enables us to work with a less complex underlying technology, which simplifies the evaluations and enhances their interpretability. Furthermore, it limits the possibility of DMUs inflating their performance by selecting extreme input‒output combinations. We demonstrate our approach with a simple numerical example and a complex data set involving Brazilian electricity distribution companies, providing clear and realistic illustrations of its application.