A new multiple criteria data envelopment analysis with variable return to scale: Applying bi-dimensional representation and super-efficiency analysis

It is known that, in general, in practical real-world problems, when the number of Decision- Making Units (DMUs) is not large enough compared to the total number of input and output parameters, the traditional DEA models with Constant Return to Scale – CRS and with Variable Return to Scale – VRS have a weak power of discrimination, producing solutions that identify many DMUs as being efficient, in addition to obtaining unrealistic weight distributions. In this context, it is recommended to work with Multiple Criteria Data Envelopment Analysis - MCDEA models. So far, all MCDEA models available in the literature adopt CRS approach. This paper proposes a New Multiple Criteria Data Envelopment Analysis (NMCDEA) – VRS model, as well as performs a super-efficiency analysis for this model. Furthermore, through bi- dimensional graphic representations, a geometric demonstration is provided, showing that, in fact, the proposed model is a good representation of situations in which it is interesting to consider a VRS behavior. The results obtained through the optimization of instances available in the literature, for real instances, as well as the sensitivity analysis carried out, indicated that the NMCDEA-VRS has a much greater power of discrimination compared to the classic DEA–VRS model.