Performance Analysis and Calculation of Marginal Rates in the Presence of Undesirable Input-output Factors and Non-Discretionary Indexes

In many production processes, the efficiency of decision-making units should be investigated in the presence of undesirable inputs and outputs and non-discretionary factors. It is also important for managers to examine the impact of changes on one index on another. Therefore, the purpose of this paper is to develop an approach to estimate the efficiency of systems with undesirable inputs and outputs and non-discretionary measures and also to analyze changes.

First, a novel approach based on data envelopment analysis was presented in order to analyze efficiency in the presence of undesirable input-output indices and non-discretionary factors. In fact, the new weak disposability axiom was used and the efficiency of the systems was investigated in the presence of undesirable input-output index and non-discretionary factors. Then the impact of changes of one non-discretionary index on another index was measured by maintaining efficiency, and the marginal rates of these changes were calculated.

In order to explain the proposed method in practice, an applied example provided based on 31 branches of Islamic Azad University (department of education) was presented and the results were discussed and analyzed. By using the suggested method, the efficiency scores and the impact of modifications were obtained.

Performance scores related to branches indicated that most of them behaved well. Also, it was observed that always increasing (decreasing) one index, while maintaining efficiency, does not end in an increase (decrease) in another index but it may remain unchanged or decreased (increased). Due to the inclusion of undesirable input and output measures and non-discretionary factors, the results of the proposed method were more acceptable than the classical DEA models.