Providing a stable hyper-efficiency model with a non-convex approach for ranking higher education centers

Traditional hyper-performance models in data envelopment analysis need detailed information about inputs and outputs. However, in many real-world problems this simple assumption does not hold. Its super-efficient stochastic models are one of the methods used to investigate the impact of uncertainty in data. One of the important assumptions in the method of random models is the certainty of the probability distribution function of imprecise data, which is hardly available in real world problems. In fact, in many problems, there is very little information from the data of the problem, which makes it impossible to estimate the probability distribution. The purpose of this evaluation is to analyze the sensitivity analysis of these academic centers when the data is imprecise.

In this research, by using the robust optimization approach, a hyper-efficient model is developed that calculates the uncertainty in the data in a multifaceted manner. Also, in the following, for the first time, the assumption of convexity was not considered in the super-efficiency model, and the stable model of super-efficiency was presented with the assumption of non-convexity.

If a unit under evaluation at one level of uncertainty has a high rating compared to other units, it will also have a high rating at other levels of uncertainty. It can also be said that more reliable results are obtained by considering the uncertainty in the data and analyzing the sensitivity of the models.