Sensitivity of super-efficient data envelopment analysis results to individual decision-making units: an example of surgical workload by specialty

We use resampling of data to explore the basic statistical properties of super–efficient data envelopment analysis (DEA) when used as a benchmarking tool by the manager of a single decision–making unit. Our focus is the gaps in the outputs (i.e., slacks adjusted for upward bias), as they reveal which outputs can be increased. The numerical experiments show that the estimates of the gaps fail to exhibit asymptotic consistency, a property expected for standard statistical inference. Specifically, increased sample sizes were not always associated with more accurate forecasts of the output gaps. The baseline DEA's gaps equaled the mode of the jackknife and the mode of resampling with/without replacement from any subset of the population; usually, the baseline DEA's gaps also equaled the median. The quartile deviations of gaps were close to zero when few decision–making units were excluded from the sample and the study unit happened to have few other units contributing to its benchmark. The results for the quartile deviations can be explained in terms of the effective combinations of decision–making units that contribute to the DEA solution. The jackknife can provide all the combinations contributing to the quartile deviation and only needs to be performed for those units that are part of the benchmark set. These results show that there is a strong rationale for examining DEA results with a sensitivity analysis that excludes one benchmark hospital at a time. This analysis enhances the quality of decision support using DEA estimates for the potential of a decision–making unit to grow one or more of its outputs.