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Abstract
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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.
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