Data Envelopment Analysis and Decision Science
Volume 2015, No. 1 (2015), Pages 58-66
Article ID dea-00095, 9 Pages
The lower limit of interval efficiency in Data Envelopment Analysis
Bijan Rahmani Parchikolaei *
Department of Mathematics, Nour Branch Islamic Azad University, Nour, Iran
* Corresponding author. Email address: firstname.lastname@example.org. Tel: +989111936760
Received: 15 December 2014; Accepted: 23 January 2015
Copyright © 2015 Bijan Rahmani Parchikolaei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In data envelopment analysis technique, the relative efficiency of the homogenous decision making units is calculated. These calculations are done based on the classical model of linear programming such as CCR,BCC,.... Because of maximizing the weighted sum of outputs to that in inputs of one unit under certain conditions, the obtained efficiency in all of these models is the upper limit of exact relative efficiency. In other words, the efficiency is calculatedfrom the optimistic viewpoint. To caculated the lower limit of efficiency, i.e. the efficiency obtained from a pessimistic viewpoint for certain weights, the existing models cannot calculate the exact lower limit and in some cases, there exist some models that show an incorrect lower limit. Through the model introduced in the present study, we can calculate the exact lower limit of the interval efficiency. The designed model can be obtained by minimizing the ratio of weighted sum of outputs to that of inputs for every unit under certion conditions. The exact lower limit can be calculated in all states through our adopted model.
Keywords: Data envelopment analysis; Interval efficiency; Interval inefficiency; lower limit; upper limit.
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