Minimum distance to efficiency frontier with integer-valued in DEA: A directional distance function approach

Conventional data envelopment analysis ( DEA ) models make the assumption of non-negativity and real values in the input and output of the systems. In many real world instances, some inputs and outputs must be integer values. The first paper in integer data is about, each point projected on the frontier is integer point and then another authors develops the axiomatic foundation for DEA in the case of in the case of integer-valued data. According to the rectified axioms presented each point can project the point close to the frontier provided and the projection point is dominated by integer point. In current paper, the authors followed the closest integer point to projection point on the frontier efficiency. According this idea, the model was presented in two phases. In the first phase, the efficiency was obtained in suitable direction and the point projected on frontier, and in the second phase, the closest integer point was found. In other words, in the second phase, the model minimized the distance of projected and integer points.