Abstract: The expected value model in stochastic data envelopment analysis (SDEA) is especially useful for evaluating the efficiency of the decision making units (DMUs) with fixed inputs and stochastic outputs. In this paper, we reinvestigate some properties of this model to extend its potential usage.
In order to identify the type of the DMUs' efficiency of the expected value model in SDEA, we first propose four types of stochastic efficiencies stochastic expected inefficiency, stochastic expected weak efficiency, stochastic expected efficiency and stochastic expected super-efficiency. We, then, develop three propositions to show the relationship between stochastic efficiency and the expected efficiency. Based on the above research findings, we demonstrate two important properties: (1) The stochastic efficiency is an increase function of the significance level when the expected efficiency remains fixed; (2) The stochastic efficiency is an increase function of the expected efficiency when the significance level remains fixed. Finally, we illustrate the above results by using stochastic simulations and a numerical example.

Key words: stochastic data envelopment analysis, decision making units, stochastic expected efficiency, expected efficiency, significance level