presentation of a two stages method to determine the suitable benchmark and return to scale (case study: girls high school of one zone shiraz city)
Subject Areas : Statistics
1 - Department of mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
Keywords: تحلیل پوششی داده ها, مجموعه مرجع کلی, بازده به مقیاس, الگو یابی,
Abstract :
In this paper, a two stages method to determine suitable benchmark and return scale of the decision making units set is presented. At first, all of the efficient reference set in no radial data envelopment analysis (DEA) based on linear programming is found. first, RAM model is introduced and units is investigated using this model, then, to run the given algorithm below steps is performed. At the first step, the type of reference set is introduced and at the second step, a unique linear programming problem based on primal dual method is proposed to know all of the possible reference sets for a decision making unit. At the third step, return to scale in the no radial DEA method is measured. Ultimately, girls high school of shiraz city one zone efficiency is investigated to show to be applicate of this method and suitable benchmark and return scale is presented for this set of decision making units.
[1] م. ر. مهرگان، مدلهای کمّی در ارزیابی عملکرد سازمانها ، تهران، دانشکده مدیریت دانشگاه تهران، چاپ دوم نشر کتاب دانشگاهی، 1391.
[2] A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operation Research, 2 (6) (1978) 429-441.
[3] A. Charnes, W. W. Cooper, E. Rhodes, Short Communication: Measuring the efficiency of decision making units, European Journal of Operational Research, 3 (1979) 339.
[4] M.J. Farrell, The Measurement of Productive Efficiency, Journal of the Royal Statistical Society. Series A (General) 120 (3) (1957) 253-290.
[5] W. W. Cooper, K. S. Park, J. T. Pastor, RAM: 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.
[6] T. Sueyoshi, K. Sekitani, Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach, European Journal Operational Research, 176 (2007) 1918-1946.
[7] V. E. Krivonozhko, F. R. Forsund, A. V. Lychev, A note on imposing strong complementary slackness conditions in DEA, European Journal of Operational Research, 220 (2012) 716-721.
[8] T. Sueyoshi, K. Sekitani, The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyper plane, European Journal of Operational Research, 181 (2007) 549-570.
[9] V. E Krivonozhko, F. R. Forsung, A. V. Lynchev, Measurement of returns to scale using non-radial DEA models, European Journal of Operation Research, 232 (2014) 664-670.
[10] W. W. Cooper, L. M. Seiford, K. Tone, Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software, Boston: Kluwer Academic Publishers, (2007).
[11] W.L. Winston, Operations Research: Applications and Algorithms, Boston: Duxbury Press, (2003).
[12] A. Charnes, W. W. Cooper, B. Golany, L. Seiford, J. Stutuz, Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical productions functions, Journal of Econometrics, 30 (1985) 91-107.
[13] K. Aida, W. W. Cooper, J.T. Pator, T. Sueyoshi, Evaluation water supply services in Japan with Ram: A range-adjusted measure of inefficiency, Omega, 26 (1998) 207-232.
[14] G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, M. Mehdillozad, I. Roshdi, connected directional slack-based measure of efficiency in DEA, Applied Mathematical Sciences, 6 (2012) 237-246.
[15] M. Mehdiloozad, B. K. Sahoo, A generalized multiplicative directional distance function for efficiency measurement in DEA, European Journal of Operational Research, 214 (2014) 679-688.
[16] R. D. Banker, A. Charnes, W. W. Cooper, Some models for the estimation of technical and scale inefficiencies in data envelopment analysis, Management science, 30 (1984) 1078-1092.
[17] J. T. Pator, J. L. Ruiz, Variables with Negative in DEA, In W. D. Cook, & Zhu (Eds.), Modeling data irregularities and structural complexities in data envelopment analysis (pp. 63-84). New York: Springer, (2007).
[18] O. B. Olesen, N. C. Petersen, Identification and use of efficient faces and facets in DEA. Journal of productivity Analysis, 20 (1996) 323-360.
[19] O. B. Olesen, N. C. Peterson, Indicators of ill-conditioned data sets and model misspecification in data envelopment analysis: An extended facet approach, Management Science, 42 (1996) 205-219.
[20] R. D. Banker, W. W. Cooper, Seiford, L. M., Thrall, R. M., Z7 Zhu, J. (2004). Returns to scale in different DEA models. European Journal of Operational Research, 154-345-362.
[21] P. L. Brockett, W. W. Cooper, L.L. Golden, J. J. Russeau, Y. Wang, Evaluating solvency versus efficiency performance and different forms of organization and marketing in US property-liability insurance companies, European Journal Operational Research, 154 (2004) 492-514.
[22] K. Tone, On returns to scale under weights restrictions in data envelopment analysis, Journal of Productivity Analysis,16 )2001(31–47.
[23] K. Tone, A simple characterization of return to scale in DEA, Journal of Operations Research Society of Japan, 39 (1996) 604–613.
[24] A. Charnes, W. W. Cooper, B. Golany, L. Seiford, J. Stutz, Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical productions functions. Journal of Econometrics, 30 (1985) 91–107.
[25] W. W. Cooper, J. T. Pastor, F. Borras, J. Aparicio, D. Pastor, BAM: A bounded adjusted measure of efficiency for use with bounded additive models, Journal of Productivity Analysis, 35 (2011) 85–94.
[26] J. T. Pastor, New additive models for handling zero and negative data (Working Paper). Spain: Universidad de Alicante, Departamento de Estadí’stica e Investigación Operativa. (1994).
[27] J. T. Pastor, J. L. Ruiz, Variables with negative values in DEA. In W. D. Cook, &
J. Zhu (Eds.), Modeling data irregularities and structural complexities in data envelopment analysis (pp. 63–84). New York: Springer. (2007).
[28] M. C. A. Silva Portela, E. Thanassoulis, Malmquist-type indices in the presence of negative data: An application to bank branches, Journal of Banking & Finance, 34 (2010) 1472–1483.
