Abstract
Traditional efficiency studies using data envelopment analysis (DEA) models considered all input and output variables as continuous, which appears to be unwarranted. Some integer-valued DEA models have been proposed for dealing with the integral constraints in many cases, such as environmental performance measurement, Olympics efficiency assessment, hotel performance evaluation and so on. In existing integer-valued DEA models, the focus is on either input-oriented projection of an inefficient DMU onto the production frontier that aims at reducing input amounts as much as possible while keeping at least the present output levels, or output-oriented projection that maximizes output levels under at most the present input consumption. The present paper develops an integer-valued DEA model that deals with input excesses and output shortfalls simultaneously in a way that maximizes both. An empirical example in the literature is re-examined to compare the DEA model developed here with existing real and integer valued approaches.
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References
Amirteimoori, A., Kordrostami, S., & Azmayande, O. H. (2007). Data envelopment analysis with selective convexity and integer-valued factors. Applied Mathematics and Computation, 188(1), 734–738.
Banker, R. J., & Morey, R. C. (1986). The use of categorical variables in data envelopment analysis. Management Science, 32(12), 1613–1627.
Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078–1092.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444.
Charnes, A., Cooper, W. W., Golany, B., Seiford, L., & Stutz, J. (1985). Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. Journal of Econometrics, 30(1–2), 91–107.
Charnes, A., Cooper, W. W., Wei, Q., & Huang, Z. M. (1989). Cone ratio data envelopment analysis and multi-objective programming. International Journal of Systems Science, 20(7), 1099–1118.
Charnes, A., Cooper, W. W., Huang, Z. M., & Sun, D. B. (1990). Polyhedral cone-ratio DEA models with an illustrative application to large commercial banks. Journal of Econometrics, 46(1–2), 73–91.
Chambers, R. G., Chung, Y., & Färe, R. (1996). Benefit and distance functions. Journal of Economic Theory, 70(2), 407–419.
Chambers, R. G., Chung, Y., & Färe, R. (1998). Profit, directional distance functions, and Nerlovian efficiency. Journal of Optimization Theory and Applications, 98(2), 351–364.
Edvardsen, D. F., & Forsund, F. R. (2003). International benchmarking of electricity distribution utilities. Resource and Energy Economics, 25(4), 353–371.
Färe, R., Grosskopf, S., Lovell, C. A. K., & Pasurka, C. (1989). Multilateral productivity comparisons when some outputs are undesirable: a nonparametric approach. Review of Economics and Statistics, 71, 90–98.
Golany, B., & Yu, G. (1997). Estimating returns to scale in DEA. European Journal of Operational Research, 103(1), 28–37.
Kamakura, W. A. (1988). A Note on the use of categorical variables in data envelopment analysis. Management Science, 34(10), 1273–1276.
Kuosmanen, T., & Matin, R. K. (2009). Theory of integer-valued data envelopment analysis. European Journal of Operational Research, 192(2), 658–667.
Liang, L., Yang, F., Cook, W. D., & Zhu, J. (2006). DEA models for supply chain efficiency evaluation. Annals of Operation Research, 145(1), 35–49.
Lins, M. P. E., Angulo, M. L., & Silva, A. C. M. (2004). A multi-objective approach to determine alternative targets in data envelopment analysis. International Journal of Operational Research, 55, 1090–1101.
Liu, W. B., Meng, W., Li, X. X., & Zhang, D. Q. (2010). DEA models with undesirable outputs. Annals of Operational Research, 173(1), 177–194.
Lozano, S., & Villa, G. (2006). Data envelopment analysis of integer-valued inputs and outputs. Computers & Operations Research, 33(10), 3004–3014.
Lozano, S., & Villa, G. (2007). Integer DEA models. In J. Zhu & W. D. Cook (Eds.), Modeling data irregularities and structural complexities in data envelopment analysis (pp. 271–290). New York: Springer.
Matin, R. K., & Kuosmanen, T. (2009). Theory of integer-valued data envelopment analysis under alternative returns to scale axioms. Omega, 37(5), 988–995.
Rousseau, J. J., & Semple, J. H. (1993). Categorical outputs in data envelopment analysis. Management Science, 39(3), 384–386.
Sakis, J. (2006). The adoption of environmental and risk management practices: Relationships to environmental performance. Annals of Operational Research, 145, 367–381.
Seiford, L. M., & Zhu, J. (2002). Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research, 142, 16–20.
Thompson, R. G., Langemeier, L. N., Lee, C. T., Lee, E., & Thrall, R. M. (1990). The role of multiplier bounds in efficiency analysis with application to Kansas farming. Journal of Econometrics, 46(1–2), 93–108.
Tone, K. (2001). A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research, 130(3), 498–509.
Wei, Q., Yan, H., & Xiong, L. (2008). A bi-objective generalized data envelopment analysis model and point-to-set mapping projection. European Journal of Operational Research, 190(3), 855–876.
Wu, J., Liang, L., Zha, Y., & Yang, F. (2009). Determination of cross-efficiency under the principle of rank priority in cross-evaluation. Expert Systems With Applications, 36(3), 4826–4829.
Wu, J., Zhou, Z., & Liang, L. (2010). Measuring the performance of nations at Beijing summer Olympics using integer-valued DEA model. Journal of Sports Economics, 11(5), 549–566.
Zenios, C., Zenios, S., Agathocleous, K., & Soteriou, A. (1999). Benchmarks of the efficiency of bank branches. Interfaces, 29(3), 37–51.
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Wu, J., Zhou, Z. A mixed-objective integer DEA model. Ann Oper Res 228, 81–95 (2015). https://doi.org/10.1007/s10479-011-0938-8
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DOI: https://doi.org/10.1007/s10479-011-0938-8