Evaluation of Multi-stage Fuzzy Networks in DEA and DEA-R Based on Liquidity Ratios with Undesirable Outputs

In this paper, radial models of multi-stage fuzzy DEA and DEA-R networks are first proposed based on liquidity ratios with desirable and undesirable outputs for evaluating a set of decision-making units (DMUs). Second, non-radial models are proposed based on the Slacks-Based Measure of Inefficiency (SBMI) and a Directional Non-Radial (DNR) model. On the one hand, the similarity of DEA and DEA-R models, as well as adherence to the axioms in constructing the production possibility set (PPS), has provided the possibility to model the restrictions of the aforementioned models; on the other hand, for efficiency calculation, different objective functions (radial and non-radial) have been used in a multi-stage network structure with fuzzy data. The models proposed for calculating the efficiency of the first, second, and third stages, as well as the overall network, in multi-stage networks therefore take the form of a fuzzy linear programming model that has been converted into linear programming. The advantage to the present article, aside from the linearity of the multi-stage fuzzy network models, is that we can model the corresponding models in DEA and DEA-R-based purely on liquidity ratios with desirable and undesirable outputs. Finally, focusing on a multi-stage network in the Iranian education system while considering fuzzy data, the efficiency and inefficiency of the DMUs are calculated based on liquidity ratios with desirable and undesirable outputs. It can be observed that in the SBMI model, the overall efficiency scores in DEA and DEA-R models are 58% and 45%, respectively.