Eciency Frontier Ideal Distance Evaluation in Presence of Integer-Values in DEA by Directional Distance Function Approach

In conventional DEA methods, all inputs and outputs are assumed to be continuous. However, the implied presumption of continuous data may not maintain an acceptable level of precision in practical data. Many practical situations such as number of teachers in a school, number of students in a college, or research papers only take integer values. Presented work presumes subsets of input and output variables in traditional ve-pronged axioms in DEA model to be integer values for the rst time in the eld. An additional eort in this work expands axioms and a new model is presented. This paper presents a novel two phase model that in the rst phase produces more precise eciency values and the best benchmark in its second phase, i.e. the nearest integer point to the eciency boundary is selected based on constant returns to scale. A case study is presented that demonstrates a comparison of eciency values obtained with this model compared to prior models that is show in table 1. an‎d in Table 2, the values of the slack are compared with each other.