Abstract
•Data envelopment analysis (DEA) is challenged by imprecise, uncertain, and stochastic data.•Two DEA adaptations (interval and robust) are developed with uncertain data and undesirable outputs.•An epsilon-based robust interval cross-efficiency model is extended.•An example and a real-world application are presented to compare our method with an interval method.•The ability of our method to improve discernibility among DMUs is demonstrated.
Degenerate optimal weights and uncertain data are two challenging problems in conventional data envelopment analysis (DEA). Cross-efficiency and robust optimization are commonly used to handle such problems. We develop two DEA adaptations to rank decision-making units (DMUs) characterized by uncertain data and undesirable outputs. The first adaptation is an interval approach, where we propose lower- and upper-bounds for the efficiency scores and apply a robust cross-efficiency model to avoid problems of non-unique optimal weights and uncertain data. We initially use the proposed interval approach and categorize DMUs into fully efficient, efficient, and inefficient groups. The second adaptation is a robust approach, where we rank the DMUs, with a measure of cross-efficiency that extends the traditional classification of efficient and inefficient units. Results show that we can obtain higher discriminatory power and higher-ranking stability compared with the interval models. We present an example from the literature and a real-world application in the banking industry to demonstrate this capability.