Effect of Relocation and Rotation on Radial Efficiency Scores for a Partially Negative Data Problem

Negative data handling has gained a remarkable importance in the literature of Data Envelopment Analysis (DEA) to address many real life problems. Various erstwhile applications, in this arena, referred relocation of the origin to a superior (RDM) or to an inferior (Translated Input Oriented BCC) neighboring point. In this paper, the conditions for Rotation Invariance of various Data Envelopment Analysis models are discussed. Specifically, in presence of partially negative data, a rotation using the Cone Ratio model, beyond a threshold value of the oblique index does not alter the efficient frontier. So, a solution can be obtained without relocating the origin. In this context, two models, termed as Input Oriented BCC model with Relocated Origin  (IOBCC-RO) and Input oriented BCC model with Rotated Axis (IOBCC-RA), are applied on a case of "the notional effluent processing system" (from Sharp et al (2006)) to observe their impact on the radial efficiency scores.