Dual Approach to Generalized Data Envelopment Analysis based on Production Possibility
So far, in order to evaluate the efficiency of DMUs, there have been developed several kinds of DEA models, for example, CCR model, BCC model, FDH model, and so on. These models are characterized by how to determine the production possibility set; a convex cone, a convex hull and a free disposable hull of observed data set. In this paper, we the GDEA D model based on production possibility as a dual approach to GDEA  and the concept of α D -efficiency in the GDEA D model. In addition, we establish the relations between the GDEA D model and existing DEA models, and interpret the meaning of an optimal value to the problem (GDEA D ). Therefore, we show that it is possible to evaluate the efficiency for each decision making unit by considering surplus of inputs/slack of outputs as well as the technical efficiency. Finally, through an illustrative example, it is shown that GDEA D can reveal domination relations among all decision snaking units.
KeywordsData Envelopment Analysis Data Envelopment Analysis Model Efficient Frontier Production Possibility Free Disposable Hull
Unable to display preview. Download preview PDF.
- 1.Belton, V. (1992) An Integrating Data Envelopment Analysis with Multiple Criteria Decision Analysis. Proceedings of the Ninth International Conference on Multiple Criteria Decision Making-Theory and Applications in Business, Industry and Commerce, eds. A. Goicoechea, L. Duckstein and S. Zoints ( Springer-Verlag, Berlin ), 71–79.Google Scholar
- 2.Belton, V., Vickers, S.P. (1993) Demystifying DEA-A Visual Interactive Approach Based on Multiple Criteria Analysis. Journal of Operational Research Society 44, 883–896.Google Scholar
- 6.Deprins, D., Simar, L., Tulkens, H. (1984) Measuring Labor-Efficiency in Post Offices, The Performance of Public Enterprises:Concepts and Measurements, eds. M. Marchand, P. Pestieu and H. Tulkens ( North Holland, Amsterdam ), 247–263.Google Scholar
- 7.Halme, M., Joro, T., Korhonen, P., Salo, A, Wallenius, J. (1999) A Value Efficiency Approach to Incorporating Preference Information in Data Envelopment Analysis, Management Science 45, 103–115.Google Scholar
- 8.Joro, T., Korhonen, P., Wallenius, J. (1998) Structural Comparison of Data Envelopment Analysis and Multiple Objective Linear Programming, Management Science 44, 962–970.Google Scholar
- 9.Stewart, T.J. (1996) Relationships Between Data Envelopment Analysis and Multiple Criteria Decision Analysis, Journal of Operational Research Society 47, 654–665.Google Scholar
- 11.Wierzbicki, H. (1980) The use of Reference Objectives in Multiobjective Optimization, Multiple Objective Decision Making, Theory and Application, eds. G. Fandel and T. Gal, Springer-Verlag, New York.Google Scholar
- 12.Yun, Y.B., Nakayama, H., Tanino, T. (2000) On efficiency of Data Envelopment Analysis, Forthcoming in Proceedings of the 14th International Conference on Multiple Criteria Decision Making, Charlottesville, Virginia, USA.Google Scholar
- 13.Yun, Y.B., Nakayama, H., Tanino, T. (1999) A Generalization of DEA Model, Journal of the Society of Instrument and Control Engineers (SICE) 35, 1813–1818.Google Scholar