A New Robust Bootstrap Algorithm for the Assessment of Common Set of Weights in Performance Analysis

Document Type : Research Paper


Department of Statistics, Faculty of Sciences, Gazi University, Ankara, Turkey


The performance of the units is defined as the ratio of the weighted sum of outputs to the weighted sum of inputs. These weights can be determined by data envelopment analysis (DEA) models. The inputs and outputs of the related (Decision Making Unit) DMU are assessed by a set of the weights obtained via DEA for each DMU. In addition, the weights are not generally common, but rather, they are very close to zero or they are even equal to zero. This means that some major criteria will not be considered. Another problem is the similarity of the efficiency scores of efficient DMUs. However, this is not the case in reality, and the performance of the DMUs should be completely ranked. Using common weights can solve these problems completely during measuring the performance of DMUs. There are some articles in the literature to determine common weight sets (CSWs), but none of them takes into account the bootstrap approach. This paper introduces a novel, empirical and robust algorithm based on bootstrapping technique to find CSWs.


Main Subjects

Article Title [Persian]

یک الگوریتم نوین بندپوتین قوی برای ارزیابی مجموعه وزنهای مشترک در تحلیل عملکرد

Authors [Persian]

  • احسان آلپ
  • ولکان سونر اوزسوی
گروه آمار، دانشکده علوم، دانشگاه غازی، آنکارا، ترکیه
Abstract [Persian]

عملکرد واحدهای تصمیم گیری (DMUs) به عنوان نسبت مجموع موزون خروجیها به مجموع موزون ورودیها تعریف می شود. این وزن ها می توانند با استفاده از مدلهای تحلیل پوششی داده ها (DEA) تعیین شوند. ورودیها و خروجیهای واحد تصمیم گیری مرتبط، توسط مجموعه ای از وزنهای به دست آمده از روش تحلیل پوششی داده ها برای هر واحد تصمیم گیری، ارزیابی می شوند. علاوه بر این، وزن ها به طور کلی مشترک نبوده، آنها خیلی نزدیک به صفر یا حتی گاهی برابر با صفر هستند. این بدین معنی است که برخی از معیارهای مهم (در ارزیابی عملکرد) در نظر گرفته نخواهند شد. مشکل دیگر امتیاز کارایی برابر برای واحدهای تصمیم گیری کارآ است. اگرچه این مطلب اغلب مورد قبول نیست و واحدهای تصمیم گیری باید به طور کامل رتبه بندی شوند. استفاده از وزن های مشترک می تواند این مشکلات را در حین اندازه گیری عملکرد واحدهای تصمیم گیری به طور کامل مرتفع نماید. اگرچه چندین مطالعه در ادبیات موضوع برای تعیین مجموعه وزنهای مشترک (CSWs) وجود دارند، اما هیچ کدام از آنها به رویکرد بندپوتین توجه نکرده اند. این مقاله یک الگوریتم جدید، بدیع ، تجربی و قوی مبتنی بر تکنیک بندپوتین برای پیدا کردن مجموعه وزنهای مشترک معرفی می کند.

Keywords [Persian]

  • تحلیل پوششی داده ها
  • مجموعه وزنهای مشترک
  • ارزیابی عملکرد
  • روش بندپوتین
Adler, N., Friedman, L., & Sinuany-Stern, Z. (2002). Review of ranking methods in the data envelopment analysis context. European journal of operational research140(2), 249-265.
Andersen, P., & Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management science39(10), 1261-1264.
Alp, İ. (2016). Another way to determine weights of balanced performance evaluations. Dumlupinar University Journal of Social Science, (Special Issue of ICEBSS), 151-161.
Angulo-Meza, L., & Lins, M. P. E. (2002). Review of methods for increasing discrimination in data envelopment analysis. Annals of Operations Research116(1-4), 225-242.
Bal, H., & Örkcü, H. H. (2011). A new mathematical programming approach to multi-group classification problems. Computers & Operations Research38(1), 105-111.
Casella, G. (2003). Introduction to the Silver Anniversary of the Bootstrap. Statistical Science18(2), 133-134.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research2(6), 429-444.
Chernick, M. R. (2008). Bootstrap methods: a guide for practitioners and researchers. New York. ISBN 978-0-471-75621-7.
Cook, W. D., & Zhu, J. (2007). Within-group common weights in DEA: An analysis of power plant efficiency. European Journal of Operational Research178(1), 207-216.
Cooper, W. W., & Tone, K. (1997). Measures of inefficiency in data envelopment analysis and stochastic frontier estimation. European Journal of Operational Research99(1), 72-88.
Daniel, W. W. (1990). Applied nonparametric statistics. Boston: Duxbury/Thomson Learning.
Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the operational research society45(5), 567-578.
Efron, B. (1982). The jackknife, the bootstrap and other resampling plans. Society for industrial and applied mathematics[H1] , Philadelphia, PA.
Efron, B., Tibshirani, R.J., (1993). An Introduction to the Bootstrap. London: Chapman and Hall.
Fisher RA. (1935). The Design of Experiments. New York: Hafner.
Friedman, L., & Sinuany-Stern, Z. (1997). Scaling units via the canonical correlation analysis in the DEA context. European Journal of Operational Research100(3), 629-637.
Ganley, J. A., & Cubbin, J. S. (1992). Public sector efficiency measurement: Applications of data envelopment analysis. North-Holland, Amsterdam[H2] , Elsevier Science Publishers.
Kao, C., & Hung, H. T. (2005). Data envelopment analysis with common weights: the compromise solution approach. Journal of the Operational Research Society56(10), 1196-1203.
Lam, K. F., & Bai, F. (2011). Minimizing deviations of input and output weights from their means in data envelopment analysis. Computers & Industrial Engineering60(4), 527-533.
Li, X. B., & Reeves, G. R. (1999). A multiple criteria approach to data envelopment analysis. European Journal of Operational Research115(3), 507-517.
Lin, R., Chen, Z., & Xiong, W. (2016). An iterative method for determining weights in cross efficiency evaluation. Computers & Industrial Engineering101, 91-102.
Liu, F. H. F., & Peng, H. H. (2008). Ranking of units on the DEA frontier with common weights. Computers & Operations Research35(5), 1624-1637.
Makui, A., Alinezhad, A., Kiani Mavi, R., & Zohrehbandian, M. (2008). A goal programming method for finding common weights in DEA with an improved discriminating power for efficiency. Journal of Industrial and Systems Engineering1(4), 293-303.
Mecit, E. D., & Alp, I. (2013). A new proposed model of restricted data envelopment analysis by correlation coefficients. Applied Mathematical Modelling37(5), 3407-3425.
Pigeot, I. (2001). The jackknife and bootstrap in biomedical research—common principles and possible pitfalls. Drug information journal35(4), 1431-1443.
Pitman, E. J. (1937). Significance tests which may be applied to samples from any populations. Supplement to the Journal of the Royal Statistical Society, 4(1), 119-130.
Pitman, E. J. G. (1938). Significance tests which may be applied to samples from any populations: III. The analysis of variance test. Biometrika, 29(3/4), 322-335.
Podinovski, V. V., & Thanassoulis, E. (2007). Improving discrimination in data envelopment analysis: Some practical suggestions. Journal of Productivity Analysis28(1-2), 117-126.
Quenouille, M. H. (1949). Approximate tests of correlation in time-series. Journal Of The Royal Statistical Society Series B-Statistical Methodology, 11(1), 68-84.
Roll, Y., Cook, W. D., & Golany, B. (1991). Controlling factor weights in data envelopment analysis. IIE transactions23(1), 2-9.
Shang, J., & Sueyoshi, T. (1995). A unified framework for the selection of a flexible manufacturing system. European Journal of Operational Research85(2), 297-315.
Sinuany-Stern, Z., & Friedman, L. (1998). DEA and the discriminant analysis of ratios for ranking units. European Journal of Operational Research111(3), 470-478.
Sinuany-Stern, Z., Mehrez, A., & Barboy, A. (1994). Academic departments efficiency via DEA. Computers & Operations Research21(5), 543-556.
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 econometrics46(1-2), 93-108.
Torgersen, A. M., Førsund, F. R., & Kittelsen, S. A. (1996). Slack-adjusted efficiency measures and ranking of efficient units. Journal of Productivity Analysis7(4), 379-398.
Troutt, M. D. (1995). A maximum decisional efficiency estimation principle. Management Science41(1), 76-82.
Wong, Y. H., & Beasley, J. E. (1990). Restricting weight flexibility in data envelopment analysis. Journal of the Operational Research Society41(9), 829-835.
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