Generalization of the RDM model in Data Envelopment Analysis

The current study extends and provides a generalization of the range directional model (RDM). The proposed generalized RDM (GRDM) model utilizes an ideal point (IP) and anti-ideal point (AIP) simultaneously to evaluate the efficiency score. It is evident that approaching to the IP, not necessarily, leads to moving away from the AIP. This obviously happens when the IP, AIP, and DMU lie on a common line; however, the depicted situation usually occurs hardly ever. On the other side, there are loads of situations in which a DMU requires not only to approach the IP but also to move away from the AIP, simultaneously. The GRDM model imposes two criteria (i.e., approaching to IP and moving away from AIP) to asses DMUs. Therefore, the efficiency score, when GRDM is used, is less than or equal to the efficiency score obtained by using the RDM model; consequently, the discrimination power of the GRDM model is better than that of the RDM model due to finding more inefficiency regarding both IP and AIP. The GRDM model is unit- and translation-invariant. A numerical example is applied to demonstrate the applicability of the proposed model in comparison with the RDM model.