A comment on a new super-efficiency model in the presence of negative data
The super-efficiency data envelopment analysis model under constant returns to scale does not suffer from the infeasibility problem while the super-efficiency model under the condition of variable returns to scale (VRS) can encounter infeasibility (Seiford and Zhu, 1999). In the presence of negative data Portela et al (2004) show that the VRS assumption is indispensable to the range directional model (RDM). In a recent paper by Hadi-Vencheh and Esmaeilzadeh (2013), (hereafter called VE), a super-efficiency model based on the RDM is formulated to establish a complete ranking of decision-making units (DMUs). The authors (2013, p. 398, Theorem 2) prove that their proposed Model (3) is feasible and bounded. However, this note shows that the VE Model (3) suffers from the common infeasibility and unboundedness problems and cannot produce the numerical results claimed. In this regard, we describe its infeasibility and unboundedness problem by means of a proposition and two counterexamples.
Citation : Pourmahmoud, J., Hatami-Marbini, A. and Babazadeh, E. (2016) A comment on a new super-efficiency model in the presence of negative data. Journal of the Operational Research Society, 67 (3), pp. 530-534
Research Institute : Centre for Enterprise and Innovation (CEI)
Peer Reviewed : Yes