A One-Step Procedure for Returns to Scale Classification of Decision Making Units in Data Envelopment Analysis

The input-output bundle of an efficient decision making unit (DMU) is located at a specific point on the frontier of the production possibility set. Returns to Scale (RTS) at this point can be unequivocally characterized. For an inefficient DMU, however, the input- and output-oriented projections on to the frontier will be different and RTS classifications at these two points may differ. In the existing literature, one needs to solve two DEA problems, one input-oriented and another output-oriented to determine the nature of RTS at these two different efficient projections. This paper shows how one can determine the returns to scale properties of an inefficient bundle simultaneously at both projections from the optimal solution of a single CCR-DEA problem either output- or input-oriented. A data set used by Christensen and Greene in their well known study of US electric utilities is used for an illustration of the proposed method in a numerical example.