A robust DEA model for measuring the relative efficiency of Iranian high schools


Mohsen Gharakhani, Ir and Hosseinali Alizadeh Haji


One of the most important issues on educational systems is to measure the relative efficiency of similar units based on non-financial factors. Data envelopment analysis (DEA) has become popular among many who wish to rank educational systems using different factors such as the rate of educational success or the number of employees, etc. However, one of the main concerns on implementing DEA methods is the uncertainty involved in input/output parameters. In this paper, a robust data envelopment analysis (RDEA) is developed to measure the efficiency of high schools considering uncertainty on output parameters. We present an empirical study on a set of high schools located in Tehran, which is the capital city of Iran. The study uses uncertain data for input/output information and the results are compared with an existing parametric stochastic frontier analysis (SFA). The preliminary results indicate that the robust DEA approach is relatively a reliable method for efficiency estimating.


DOI: j.msl.2011.01.002

Keywords: Data envelopment analysis ,Robust optimization ,Stochastic frontier analysis ,High schools efficiency ducational economics ,

How to cite this paper:

Gharakhani, M., Ir, I & Haji, H. (2011). A robust DEA model for measuring the relative efficiency of Iranian high schools.Management Science Letters, 1(3), 389-404.


References

Aigner, D., & Chu, S. (1968). On estimating the industry production function. The American Economic Review, 58(4), 826-839.

Aigner, D., Lovell, C., & Schmidt, P. (1977). Formulation and Estimation of Frontier Production, Profit and Cost Functions. Journal of econometrics, 6(1), 21-37.Bagi, F., & Huang, C. (1983). Estimating production technical efficiency for individual farms in Tennessee. Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, 31(2), 249-256.Barrow, M. (1991). Measuring local education authority performance: a frontier approach. Economics of Education Review, 10(1), 19-27.

Battese, G., & Coelli, T. (1988). Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data* 1. Journal of econometrics, 38(3), 387-399.Battese, G., & Corra, G. (1977). Estimation of a production frontier model: with application to the pastoral zone of Eastern Australia. Australian Journal of Agricultural Economics, 21(3), 169-179.

Ben-Tal, A., & Nemirovski, A. (1998). Robust convex optimization. Mathematics of Operations Research, 23(4), 769-805.

Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions of uncertain linear programs. Operations Research Letters, 25(1), 1-14.

Ben-Tal, A., & Nemirovski, A. (2000). Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming, 88(3), 411-424.

Bertsimas, D., & Sim, M. (2003). Robust discrete optimization and network flows. Mathematical Programming, 98(1), 49-71.

Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52(1), 35-53.

Bertsimas, D., & Sim, M. (2006). Tractable approximations to robust conic optimization problems. Mathematical Programming, 107(1), 5-36.

Bertsimas, D., Pachamanova, D., & Sim, M. (2004). Robust linear optimization under general norms. Operations Research Letters, 32(6), 510-516.

Bessent, A., & Bessent, E. (1980). Determining the comparative efficiency of schools through data envelopment analysis. Educational Administration Quarterly, 16(2), 57.Bessent, A., Bessent, W., Kennington, J., & Reagan, B. (1982). An application of mathematical programming to assess productivity in the Houston independent school district. Management Science, 28(12), 1355-1367.

Bonesrqnning, H., & Rattsq, J. (1994). Efficiency variation among the Norwegian high schools: consequences of equalization policy. Economics of Education Review, 13(4), 289-304.

Charnes, W. (1978). Measuring the efficiency of decision making units* 1. European journal of operational research, 2(6), 429-444.Coelli, T. (1994). A guide to FRONTIER version 4.1: a computer program for stochastic frontier production and cost function estimation. Department of Econometrics, University of New England, Armidale, Australia.Coelli, T., & Perelman, S. (1999). A comparison of parametric and non-parametric distance functions: With application to European railways. European journal of operational research, 117(2), 326-339.Cooper, S., & Cohn, E. (1997). Estimation of a frontier production function for the South Carolina educational process. Economics of Education Review, 16(3), 313-327.

El-Ghaoui, L., & Lebret, H. (1997). Robust solutions to least-square problems to uncertain data matrices. SIAM J. Matrix Anal. Appl, 18, 1035-1064.

Falk, J. (1976). Exact solutions of inexact linear programs. Operations Research, 24(4), 783-787.

Färe, R., Grosskopf, S., & Weber, W. (1989). Measuring school district performance. Public Finance Review, 17(4), 409.Forsund, F., Lovell, C., & Schmidt, P. (1980). A survey of frontier production functions and of their relationship to efficiency measurement. Journal of econometrics, 13(1), 5-25.Grosskopf, S., Hayes, K., Taylor, L., & Weber, W. (1997). Budget-constrained frontier measures of fiscal equality and efficiency in schooling. Review of Economics and Statistics, 79(1), 116-124.

Jesson, D., Mayston, D., & Smith, P. (1987). Performance assessment in the education sector: educational and economic perspectives. Oxford Review of Education, 13(3), 249-266.

Jondrow, C. (1982). On the estimation of technical inefficiency in the stochastic frontier production function model* 1. Journal of econometrics, 19(2-3), 233-238.

Kalirajan, K., & Flinn, J. (1983). The measurement of farm specific technical efficiency. Pakistan Journal of Applied Economics, 2(2), 167-180.

Klitgaard, R., & Hall, G. (1975). Are there unusually effective schools? Journal of Human Resources, 90-106.Kumbhakar, S., Ghosh, S., & McGuckin, J. (1991). A generalized production frontier approach for estimating determinants of inefficiency in US dairy farms. Journal of Business & Economic Statistics, 9(3), 279-286.

Lee, L., & Tyler, W. (1978). The stochastic frontier production function and average efficiency: An empirical analysis. Journal of econometrics, 7(3), 385-389.Levin, H. (1974). Measuring efficiency in education production”. Public Finance Quaterly, 2, 2-24.

Levin, H., Jamison, D., & Radner, R. (1976). Concepts of economic efficiency and educational production. NBER Chapters, 149-198.

Ludwin, W., & Guthrie, T. (1989). Assessing productivity with data envelopment analysis. Public Productivity Review, 12(4), 361-372.

McCarty, T., & Yaisawarng, S. (1993). Technical efficiency in New Jersey school districts. The measurement of productive efficiency: techniques and applications, 271-287.

Meeusen, W., & van Den Broeck, J. (1977). Efficiency estimation from Cobb-Douglas production functions with composed error. International Economic Review, 435-444.

Pitt, M., & Lee, L. (1981). The measurement and sources of technical inefficiency in the Indonesian weaving industry. Journal of Development Economics, 9(1), 43-64.

Ray, S. (1991). Resource-use efficiency in public schools: A study of Connecticut data. Management Science, 37(12), 1620-1628.

Sadjadi, S., & Omrani, H. (2008). Data envelopment analysis with uncertain data: An application for Iranian electricity distribution companies. Energy Policy, 36(11), 4247-4254.

Schmidt, P., & Sickles, R. (1984). Production frontiers and panel data. Journal of Business & Economic Statistics, 2(4), 367-374.

Simar, L., & Wilson, P. (1998). Sensitivity analysis of efficiency scores: How to bootstrap in nonparametric frontier models. Management Science, 44(1), 49-61.

Simar, L., & Wilson, P. (2000). A general methodology for bootstrapping in non-parametric frontier models. Journal of Applied Statistics, 27(6), 779-802.

Soyster, A. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research, 21(5), 1154-1157.

Waldman, D. (1984). Properties of technical efficiency estimators in the stochastic frontier model. Journal of econometrics, 25(3), 353-364.Wyckoff, J., & Lavinge, J. (1991). The Relative Inefficiency of Public Elementary Schools in New York. In: Working Paper, State University of New York, Albany.

Zhu, J. (1998). Data envelopment analysis vs. principal component analysis: An illustrative study of economic performance of Chinese cities. European journal of operational research, 111(1), 50-61.