Inverse DEA Model with Fuzzy Data for Output Estimation
Subject Areas : Data Envelopment AnalysisA. Mahmoodi Rad 1 , R. Dehghan 2 , F. Hosseinzadeh Lotfi 3
1 - Department of Mathematics, Islamic Azad University, MasjedsoleimanBranch, Iran
2 - Department of Mathematics, Islamic Azad University, MasjedsoleimanBranch, Iran
3 - Department of Mathematics, Islamic Azad University, Science & ResearchBranch, Tehran, Iran
Keywords: Data envelopment analysis, Multi-objective programming, fuzzy numbers, Inverse DEA Model,
Abstract :
In this paper, we show that inverse Data Envelopment Analysis (DEA) modelscan be used to estimate output with fuzzy data for a Decision Making Unit (DMU)when some or all inputs are increased and deficiency level of the unit remainsunchanged.
[1] Banker R. D., Charnes A., Cooper W.W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management science, 30, 1078-1092, 1984.
[2] Bazaraa M. S., Jarvis J. J., and Sherali H. D., Linear programming and network flows, John Wiley, New York, second edition 1990.
[3] Charnes A., Cooper W.W. , and Rhodes E., Measuring the efficiency of decision making units, European Journal of Operational Research, 429-444, 1978.
[4] Charnes A., Cooper W.W., Lewin A.Y., and Seiford L.M., Data envelopment Analysis- Theory, Methodology and Applications, Kluwer Academic Publishers, Boston 1994.
[5] Joro R., Korhonen P., Wallenius J., Structural comparison of data envelopment analysis and multiple objective linear programming , Management science, 44(7), 926- 970, 1999.
[6] Joro R., Korhonen P., Zionts S., An interactive approach to improve estimates of value efficiency in data envelopment analysis, European Journal of operational research,149, 688-699, 2003.
[7] Klir G. J., Yuan B., Fuzzy sets and fuzzy logic: Theory and Applications, Prentice- Hall, India 2001.
[8] Maleki H. R., Tata M., Mashinchi M., Linear programming with fuzzy variables, Fuzzy sets and systems, 109 , 21-33, 2000.
[9] Wei Q., Zhang L.J., and Zhang X., An inverse DEA models for input/output estimate, European Journal of Operational Research 121(1), 151-163, 2000.
[10] Wong B. Y. H., Luque M., Yang J. B., Using interactive multi objective methods to solve DEA problems with value judgments, Computers and Operations research, 36, 623-636, 2009.
[11] Zimmermann H. J., Fuzzy set theory and its application, Kluwer Academic publishers, London 1996.