Decisional performance efficiencies of cross-efficiency DEA decision-making units using benevolent criterion

This paper uses the maximum decisional efficiency (MDE) principle to rank decisional performance efficiencies of cross-efficiency (CE) data envelopment analysis (DEA) decision-making units (DMUs) that use benevolent criterion. Under the benevolent criterion, each DMU independently selects a set of common weights to maximize the average peer efficiency scores. The performance of each DMU in selecting the set of common weights is called the decisional performance efficiency (DPE) of the DMU. The DPEs of all DMUs are assumed to be distributed as a monotone increasing probability density function (pdf) of unknown parameters. A maximum-likelihood (ML) approach using a genetic algorithm is used to learn the parameters of the pdf. Once the underlying parameters of the pdf are known, DPEs can be computed and the DMUs can be ranked based on their DPEs. Additionally, the Markov Chain Monte Carlo technique can be applied to establish confidence interval bounds on the ML parameter describing the MDE pdf. Three examples using datasets from the literature are provided.