Farzad Rezai Balf - Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
Reza Shahverdi - Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
Maryam Hatefi - Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Data Envelopment Analysis (DEA), a popular linear programming technique is useful to rate comparatively operational effiency of decision Making Unit (DMU) based on the their deterministic input-output data. The Malmquist productivity index in DEA, calculable with the distance function, for measurement the productivity change among two variant time period or two the variant group in the same time. This index is based on two factor of efficiency change index and a technological change index. In this paper, we operates on the collective Malmquist productivity index, which perform clustering operation DMUs with classification into different levels of efficient frontier, and then discusses on the relation between Malmquist index on the efficiency layers and their attractiveness and progress.

Data envelopment analysis, Efficiency layers,Malmquist productivity index, Attractiveness and progress