Developing a robust model of non-homogeneous mixed NDEA with open structure at each stage and interlayer connection

This paper aims to develop a non-homogeneous NDEA model for measuring the efficiency of a mixed network with an open structure at each stage, interlayer connections, and uncertainties in inputs, outputs, and intermediate processes. 

To model the problem, a new model has been proposed first to determine the efficiency of each layer, based on the average weight of the layers. Then, the model has been developed to calculate the total efficiency. The Bertismas and Sim approach has been used to consider the uncertainty of inputs, outputs, and intermediate processes. Pistachio orchards in Yazd province have been selected as a case study, and relevant data of 10 cities in the Yazd province has been collected from the Agricultural Jihad Organization of Yazd province. 

The results indicated that with increasing the deviation in uncertain network data from 0.01 to 0.1, the average total efficiency decreased from 0.933 to 0.915. Such a reduction was also observed in the efficiency score of each of the DMUs. Reducing the average levels of efficiency and tightening the constraints on the proposed models reduced the number of units on the Performance boundary and eliminated the need to use super-efficient models to re-evaluate the efficiency. In other words, the computation of the total efficiency of decision-making units and sub-layers was enhanced. Research limitations/implications : The proposed approach was developed based on the model of Charans et al. (1978). As a limitation, the weighted sum of the outputs was less than or equal to the weighted sum of the inputs. The proposed model can be developed further to include other factors, such as undesirable outputs.

Findings can provide a more accurate understanding of the performance of the components of decision-making units to managers and decision-makers. This study highlights the usefulness of the proposed models as a decision tool in agricultural units. 

The developed models can be used in various social contexts. According to the case study, it is overemphasized that water resources management is significantly important for Yazd as a province located in an arid and desert region. Therefore, increasing the efficiency of orchards by identifying and improving inefficient processes, can lead to helpful-agricultural consequences in this province. 

While many studies have been conducted in the field of NDEA, this is the first study in the field of open non-homogeneous mixed networks considering uncertainty in all data, simultaneously.