A novel robust data envelopment analysis with asymmetric uncertainty and an application to National Basketball Association

While data availability provides adequate support for decision-making, asymmetrically distributed uncertainty remains an inevitable factor in the decision-making process. Robust data envelopment analysis (RDEA) is one of the most popular methods to handle uncertainty in input and output data. However, previous RDEA studies assume that the uncertainty of the data is symmetrically distributed, which is often violated in practical applications, such as in sports and finance. This paper aims to relax that assumption and extend RDEA models to more general scenarios. To this end, this paper proposes a new RDEA method that can capture asymmetrically distributed uncertainties from historical data and can be easily solved. In addition, a comprehensive case study of player efficiency evaluation is conducted to illustrate the merits of the proposed method. The contributions can be concluded as follows. This study introduces a novel approach to considering asymmetrically distributed uncertainty sets in the RDEA domain, which has not been previously explored. The proposed model outperforms existing RDEA models, providing more reliable and complete ranking results. Additionally, we demonstrate a comprehensive data-driven application that showcases how to build uncertainty sets from historical data and utilize our RDEA model for efficiency evaluation. Furthermore, our model's flexibility allows decision-makers to adjust its conservativeness according to their preferences, offering more dependable results. By utilizing our proposed model, decision-makers can make better-informed decisions while also receiving guidance on how to enhance the reliability of their results.