Attractiveness and Progress in Integer-Valued Data Envelopment Analysis

Document Type : Original Article


1 Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.

2 Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran.


Data envelopment analysis (DEA) is a non-parametric technique to measure and evaluating the relative efficiencies of the set of homogenous decision making units (DMUs) with multiple inputs and multiple outputs. Traditional DEA models assume that inputs and outputs to be continuous, real-valued data. In many occasions, inputs or outputs can only take integer values. Therefore, DEA models can not be used for determining efficiency score of DMUs. The current paper applies of the modified classic DEA models to obtain attractiveness and progress in integer-valued technologies. For this aim, in the first phase, the efficiency score of all DMUs are measured and the efficient and inefficient units are determined. Then, in the second phase, we remove the main efficient frontier that corresponds to the efficient units, and then we create a new efficient frontier as the second layer efficient frontier of the remaining units (units inefficient). With repeat this process, we find the next layers until there is no any unit left. Finally, the attractiveness and progress of each unit is calculated from one efficient level relative to the other efficient level.