The ideal distance to efficiency frontier with integer-valued in DEA

In traditional Data Envelopment Analysis (DEA) all inputs and outputs are assumed to take real values. However, this is not realistic in many practical situations and in some applications we may need to work with integer variables and parameters. Once we assume that the variables can take only integer values, we may need to review different concepts of DEA. The first paper is noted about integer data ,due to each point that projected on the frontier is integer point and according to this theory exhibited axioms and then some of these axioms are rectified. according to rectified axioms presented paper that each point can projected the point close the frontier provided that the projection point dominated with integer point.in this paper, by intended axioms have extended model that minimize the distance of projected point to frontier.in other words, we project the intended point that have minimum distance from the frontier as long as the projection point dominates with integer point. With an example, we check out our model with past models.an empirical example illustrate the approach.