Abstract
Data Envelopment Analysis (DEA) is widely used as a tool to measure the eciency of a set of decision making units(DMUs). Traditional DEA requires observations to be deterministic while many of them are stochastic in practice and this results that eciencies are stochastic as well. In that case, conclusions based on traditional DEA could be misleading because the realized level of stochastic data is sensitive to eciency scores. In this paper, we develop a sequential sampling method to fi nd optimal sample sizes of each DMU to estimate random inputs or outputs in a cost e ective way. The gap of estimated eciency scores between true ones are guaranteed to fall in a small interval. Furthermore, the quality of eciency scores and the feasibility of solutions are assured by statistical theories. We illustrate the proposed method by performing an Automated Guided Vehicle System (AGVS) to identify e ective alternatives with two input factors: the number of vehicles and the load capacity of single vehicle. The eciency interval and the sample size of each DMU are obtained to observe their scores. The numerical results present the viability and the e ectiveness of our proposed method.