A Robust Data Envelopment Analysis for Evaluating Technical Efficiency of Indonesian High Schools

U. Mahmudah, S. Suhartono, A. D. Rohayana


The main purpose of this study is to evaluate the technical efficiency of high school education in Indonesia by applying Data Envelopment Analysis (DEA), which is the most frequently used to measure the efficiency scores. However, this study uses a robust approach to face the complex problem of the traditional DEA, which may lead to biased results. Besides, it is a powerful approach to estimate technical efficiency when outliers contaminate the data set. Statistical data from general senior secondary schools in the period 2015/2016 is analyzed, using 34 provinces as decision-making units (DMUs), with eight input and six output variables. The results indicate that the average efficiency score of Indonesia’s major political subdivisions in managing high school education is 0.936. Furthermore, as many as 32.35 percents of provinces achieve efficient performances, with an efficiency score equal to one, while 17 provinces have above average efficiency scores.  The results also indicate that efficiency scores from robust data envelopment analysis provide better accuracy. Overall, application of robust data envelopment analysis (RDEA) is appropriate for measuring the efficiency of provincial performance in organizing secondary education.


DEA; efficiency;robust;outliers

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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.

Barrow, M. M. (1991). Measuring local education authority performance: a frontier approach. Economics of Education Review, 10(1), 19-27.

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(1-3), 49-71.

Besstremyannaya, G., Simm, J., & Golovan, S. (2014). Robust non-parametric estimation of cost efficiency with an application to banking industry. Working paper.

Bonesrønning, H., & Rattsø, J. (1994). Efficiency variation among the Norwegian high schools: consequences of equalization policy. Economics of education review, 13(4), 289-304.

Carrington, R., Coelli, T. I. M., & Rao, D. S. (2005). The performance of Australian universities: Conceptual issues and preliminary results. Economic Papers: A journal of applied economics and policy, 24(2), 145-163.

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., Haag, S., Jaska, P., & Semple, J. (1992). Sensitivity of efficiency classifications in the additive model of data envelopment analysis. International Journal of Systems Science, 23(5), 789-798.

Coelli, T. J., Rao, D. S. P., O’Donnell, C. J., & Battese, G. E. (2005). An introduction to efficiency and productivity analysis. Springer Science & Business Media.

Cooper, S. T., & Cohn, E. (1997). Estimation of a frontier production function for the South Carolina educational process. Economics of Education Review, 16(3), 313-327.

Cooper, W. W., Huang, Z., Lelas, V., Li, S. X., & Olesen, O. B. (1998). Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. Journal of Productivity Analysis, 9(1), 53-79.

Dwianto, A., Wilujeng, I., Prasetyo, Z. K., & Suryadarma, I. G. (2017). The Development of Science Domain Based Learning Tool Which is Integrated with Local Wisdom to Improve Science Process Skill and Scientific Attitude. Jurnal Pendidikan IPA Indonesia, 6(1), 23-31.

Efron, B. (1979). Bootstrap methods: another look at the jackknife annals of statistics 7: 1–26. View Article PubMed/NCBI Google Scholar.

Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society. Series A (General), 120(3), 253-290.

Fatimah, S., & Mahmudah, U. (2017). Two-Stage Data Envelopment Analysis (DEA) for Measuring the Efficiency of Elementary Schools in Indonesia. International Journal of Environmental and Science Education.

Gstach, D. (1998). Another approach to data envelopment analysis in noisy environments: DEA+. Journal of Productivity Analysis, 9(2), 161-176.

Kong, W. H., & Fu, T. T. (2012). Assessing the performance of business colleges in Taiwan using data envelopment analysis and student based value-added performance indicators. Omega, 40(5), 541-549.

Mikušová, P. (2015). An application of DEA methodology in efficiency measurement of the Czech public universities. Procedia Economics and Finance, 25, 569-578.

Ministry of Education and Culture of Republic of Indonesia. 2016. Nilai Rata-rata Sekolah UN. Retrieved from https://data.go.id/dataset/nilai-rata-rata-sekolah-un.

Nazarko, J., & Šaparauskas, J. (2014). Application of DEA method in efficiency evaluation of public higher education institutions. Technological and Economic development of Economy, 20(1), 25-44.

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

Simar, L., & Wilson, P. W. (2007). Estimation and inference in two-stage, semi-parametric models of production processes. Journal of econometrics, 136(1), 31-64.

Suhardi, D. (2017). Statistik Persekolahan Sekolah Menengah Atas (SMA) 2016/2017.

Thanassoulis, E., Dyson, R. G., & Foster, M. J. (1987). Relative efficiency assessments using data envelopment analysis: an application to data on rates departments. Journal of the Operational Research Society, 38(5), 397-411.

Wilson, P. W. (1995). Detecting influential observations in data envelopment analysis. Journal of productivity analysis, 6(1), 27-45.

Yusrizal, Y., Suliyanah, S., & Basri, T. H. (2017). Analysis of Knowledge, Understanding and Skills of Physics Teachers of State Senior High Schools in Developing and Analyzing Test Items. Jurnal Pendidikan IPA Indonesia, 6(2), 335-340.

Zhu, J. (1996). Robustness of the efficient DMUs in data envelopment analysis. European Journal of operational research, 90(3), 451-460.


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