One of the well-known ranking methods in Data Envelopment Analysis is the cross-efficiency ranking method. This method is frequently used under the assumption of constant returns to scale. However, due to the fact that negative VRS efficiencies may be apparent in the traditional input-oriented cross-efficiency method, this method is rarely used under the assumption of variable returns to scale (VRS). There exist a few studies to address the aforementioned issue. Nonetheless, a remarkable point is that all of them change the efficiency frontier of the production possibility set (PPS) and this change can reduce their results’ validity. In this paper, using a geometric interpretation, it is shown that each cross-efficiency quantity corresponds to a particular distance measure. Therefore, based on the aforementioned distance measure, the cross-efficiency method is developed under the assumption of VRS.
