Recognizing the efficiency, weak efficiency and inefficiency of DMUs with an epsilon independent linear program

One of the important problems in the CCR and BBC models is determining the non-Archimedean infinitesimal epsilon. Mehrabian et al. [S. Mehrabian, G.R. Jahanshahloo, M.R. Alirezaei, G.R. Amin, An assurance interval for the non-Archimedean Epsilon in DEA models, Operations Research 48(2) (2000) 344-347] presented a procedure for determining overall assurance interval of ε. They also showed that choosing ε in this interval guarantees the feasibility/boundedness of the multiplier/envelopment side of CCR models. In this paper we show that choosing ε arbitrarily in the proposed overall assurance interval may not lead to correct recognition of the efficient and inefficient DMUs. Then we propose a new model that can recognize the efficient and inefficient DMUs without dependence on different values of ε.