Ranking DMUs by Ideal PPS in Data Envelopment Analysis
An original DEA model is to evaluate each DMU
optimistically, but the interval DEA Model proposed in this paper
has been formulated to obtain an efficiency interval consisting of
Evaluations from both the optimistic and the pessimistic view points.
DMUs are improved so that their lower bounds become so large as to
attain the maximum Value one. The points obtained by this method
are called ideal points. Ideal PPS is calculated by ideal of efficiency
DMUs. The purpose of this paper is to rank DMUs by this ideal PPS.
Finally we extend the efficiency interval of a DMU under variable
RTS technology.
[1] A. Charnes, W.W. Cooper, E. Rhodes, Measuring the efficiency of
decision making units, European Journal of Operational Research 2
(1978) 429444.
[2] A. Charnes, W.W. Cooper, E. Rhodes, Evaluating program and
managerial efficiency: An application of data envelopment analysis to
program follows through, Management Science 27 (6) (1981) 668734.
[3] F. Nagano, T. Yamaguchi, T. Fukukawa, DEA with fuzzy output data,
Communications of the Operational Research Society of Japan
40(8)(1995), 425-429 (in Japanese).
[4] G.R. Jahanshahloo, F. Hosseinzadeh Lotfi, N. Shoja, G. Tohidi, S.
Razavyan, Ranking using l1-norm in data envelopment analysis, Applied
Mathematics and Computation 153(2004) 215-224.
[5] K. Tone, A slacks based measure of efficiency in data envelopment
analysis. European Journal of Operational Research 130(2001) 498-509.
[6] R.Fare ,C.A.K. Lovel, Measuring the technical efficiency of production.
Journal of Economic Theory 19(1978) 150-162.
[7] R.R. Russell, Measure of technical efficiency. Journal of Economic
Theory 35(1985) 109-126.
[8] P. Andersen, N.C. Petersen, A procedure for ranking efficient units in
data envelopment analysis,Management Science 39(1993) 1261-1264.
[9] S. Mehrabian, M.R. Alirezaee, G.R. Jahanshahloo, A complete
efficiency ranking of decision making units in data envelopment
analysis, Computational Optimization and Applications 14(1999)261-
266.
[10] T. Entani, Y. Maeda, H. Tanaka, Dual models of interval DEA and its
extension to interval data, European Journal of Operational Research
136(2002) 32-45.
[11] T. Entani, H. Tanaka, Improvement of efficiency intervals based on
DEA by adjusting inputs and outputs, European Journal of Operational
Research 172 (2006) 1004-1017.
[12] T. Sueyoshi, K. Sekitani, Computational strategy for Russell measure in
DEA. European Journal of Operational Research 180(2007) 459-471.
[13] W.W. Cooper, K.S. Park, J.T. Pastor, A range adjusted measure of
inefficiency for use with additive models and relations to other models
and measures in DEA. Journal of Productivity Analysis 11(1999) 5-42.
[14] W.W. Cooper, J.T. Pastor, Efficiency aggregation with enhanced Russel
measure in DEA Working Paper. University of Texas at Austin, TX
78712-1174, USA (2003).
[15] Y.-M.Wang, R. Greatbanks, J.-B. Yang, Interval efficiency assessment
using data envelopment analysis. Fuzzy Sets and Systems 153(2005)
347-370.
[1] A. Charnes, W.W. Cooper, E. Rhodes, Measuring the efficiency of
decision making units, European Journal of Operational Research 2
(1978) 429444.
[2] A. Charnes, W.W. Cooper, E. Rhodes, Evaluating program and
managerial efficiency: An application of data envelopment analysis to
program follows through, Management Science 27 (6) (1981) 668734.
[3] F. Nagano, T. Yamaguchi, T. Fukukawa, DEA with fuzzy output data,
Communications of the Operational Research Society of Japan
40(8)(1995), 425-429 (in Japanese).
[4] G.R. Jahanshahloo, F. Hosseinzadeh Lotfi, N. Shoja, G. Tohidi, S.
Razavyan, Ranking using l1-norm in data envelopment analysis, Applied
Mathematics and Computation 153(2004) 215-224.
[5] K. Tone, A slacks based measure of efficiency in data envelopment
analysis. European Journal of Operational Research 130(2001) 498-509.
[6] R.Fare ,C.A.K. Lovel, Measuring the technical efficiency of production.
Journal of Economic Theory 19(1978) 150-162.
[7] R.R. Russell, Measure of technical efficiency. Journal of Economic
Theory 35(1985) 109-126.
[8] P. Andersen, N.C. Petersen, A procedure for ranking efficient units in
data envelopment analysis,Management Science 39(1993) 1261-1264.
[9] S. Mehrabian, M.R. Alirezaee, G.R. Jahanshahloo, A complete
efficiency ranking of decision making units in data envelopment
analysis, Computational Optimization and Applications 14(1999)261-
266.
[10] T. Entani, Y. Maeda, H. Tanaka, Dual models of interval DEA and its
extension to interval data, European Journal of Operational Research
136(2002) 32-45.
[11] T. Entani, H. Tanaka, Improvement of efficiency intervals based on
DEA by adjusting inputs and outputs, European Journal of Operational
Research 172 (2006) 1004-1017.
[12] T. Sueyoshi, K. Sekitani, Computational strategy for Russell measure in
DEA. European Journal of Operational Research 180(2007) 459-471.
[13] W.W. Cooper, K.S. Park, J.T. Pastor, A range adjusted measure of
inefficiency for use with additive models and relations to other models
and measures in DEA. Journal of Productivity Analysis 11(1999) 5-42.
[14] W.W. Cooper, J.T. Pastor, Efficiency aggregation with enhanced Russel
measure in DEA Working Paper. University of Texas at Austin, TX
78712-1174, USA (2003).
[15] Y.-M.Wang, R. Greatbanks, J.-B. Yang, Interval efficiency assessment
using data envelopment analysis. Fuzzy Sets and Systems 153(2005)
347-370.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:49162", author = "V.Rezaie and M.Khanmohammady", title = "Ranking DMUs by Ideal PPS in Data Envelopment Analysis", abstract = "An original DEA model is to evaluate each DMU
optimistically, but the interval DEA Model proposed in this paper
has been formulated to obtain an efficiency interval consisting of
Evaluations from both the optimistic and the pessimistic view points.
DMUs are improved so that their lower bounds become so large as to
attain the maximum Value one. The points obtained by this method
are called ideal points. Ideal PPS is calculated by ideal of efficiency
DMUs. The purpose of this paper is to rank DMUs by this ideal PPS.
Finally we extend the efficiency interval of a DMU under variable
RTS technology.", keywords = "Data envelopment analysis (DEA), Decision makingunit (DMU), Interval DEA, Ideal points, Ideal PPS, Return to scale(RTS).", volume = "4", number = "7", pages = "538-6", }