Abstract
In data envelopment analysis (DEA), input and output values are subject to change for several reasons. Such variations differ in their input/output items and their decision-making units (DMUs). Hence, DEA efficiency scores need to be examined by considering these factors. In this paper, we propose new resampling models based on these variations for gauging the confidence intervals of DEA scores. The first model utilizes past-present data for estimating data variations imposing chronological order weights which are supplied by Lucas series (a variant of Fibonacci series). The second model deals with future prospects. This model aims at forecasting the future efficiency score and its confidence interval for each DMU. We applied our models to a dataset composed of Japanese municipal hospitals.
Highlights
data envelopment analysis (DEA) is a non-parametric methodology for performance evaluation and benchmarking
The first practical issue is the lack of a statistical foundation for DEA which was laid down by Banker [2] who proved that DEA models could be viewed as maximum likelihood estimation models under specific conditions and Banker and Natarajan [3] proved that
Charnes and Neralić [4] and Neralić [5] used conventional linear programming-based sensitivity analysis under additive and multiplicative changes in inputs and/or outputs to investigate the conditions under which the efficiency status of an efficient decision-making units (DMUs) is preserved, whereas Zhu [6] performed sensitivity analysis using various super-efficiency DEA models in which a test DMU is not included in the reference set
Summary
DEA is a non-parametric methodology for performance evaluation and benchmarking. Since the publication of the seminal paper by Charnes, Cooper and Rhodes [1], DEA has witnessed numerous developments, some of which are motivated by theoretical considerations and others motivated by practical considerations. Charnes and Neralić [4] and Neralić [5] used conventional linear programming-based sensitivity analysis under additive and multiplicative changes in inputs and/or outputs to investigate the conditions under which the efficiency status of an efficient DMU is preserved (i.e., basis remains unchanged), whereas Zhu [6] performed sensitivity analysis using various super-efficiency DEA models in which a test DMU is not included in the reference set This sensitivity analysis approach simultaneously considers input and output data perturbations in all DMUs, namely, the change of the test DMU and the remaining DMUs. On the other hand, several authors investigated the sensitivity of DEA scores to the estimated efficiency frontier.
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