Data envelopment analysis in satisfaction survey research: sample size problem

Data envelopment analysis (DEA) frequently uses stochastic input and/or output data. If these data are estimated from a sample in each decision-making unit, the DEA efficiency will be an estimation of the obtained efficiency if the population information is available. We propose a methodology to determine the relationship between the sample size and the estimation error of the efficiency in the presence of output data estimated with a sample. The practical utility of this result is to evaluate, with fixed precision, the efficiency of a set of making units, taking deterministic inputs that explain the opinion-satisfaction of the unit users, whose opinion is known through a sampling survey. We illustrate how to apply the proposed research with a case study.