Distance optimization approach to ratio-form efficiency measures in data envelopment analysis

Abstract

The standard data envelopment analysis measures of the Charnes–Cooper–Rhodes (CCR) and slacks-based measure (SBM) are ratio-form efficiency measures, which do not yield the closest projections. However, because of difficulties implementing projections based on standard measures, the closest projections identified by means of least-distance measures may be preferable. Taking into account the practical significance of closest projection points, Aparicio et al. (J Prod Anal 28:209–218, 2007) proposed a least-distance approach based not only on the 1-norm (Manhattan), 2-norm (Euclidean), and ∞-norm (Chebyshev), but also on the procedure presented by Cherchye and Van Puyenbroeck (Eur J Oper Res 132(2):287–295, 2001). Recently, Tone (Eur J Oper Res 200(2):901–907, 2010) presented a least-distance version of SBM (or equivalently, the enhanced Russell graph measure). However, these authors examined neither the occurrence of multiple optimal projections nor the strong/weak monotonicity of the ratio-form least-distance efficiency measures over the efficient frontier of the production technology. Furthermore, it is not well known that the standard measures of CCR and SBM suffer from the occurrence of multiple optimal solutions or efficient targets. Therefore, the present paper also investigates the possibility of multiple optimal targets and axiomatic properties of ratio-form efficiency measures within a unified p-norm efficiency measurement framework.