The Comparison of Principal Component Analysis and Data Envelopment Analysis in Ranking of Decision Making Units

Year 2006, Volume: 19 Issue: 2, 127 - 133, 29.03.2010

Filiz Kardıyen H.hasan Örkcü

Abstract

In this study, Data Envelopment Analysis (DEA) and Principal Component Analysis (PCA) were compared when these two methods are used for ranking Decision Making Units (DMU) with multiple inputs and outputs. DEA, a nonstatistical technique, is a methodology using a linear programming model for evaluating and ranking DMU’s performance. PCA, a multivariate statistical method, uses new measures defined by DMU’s inputs and outputs. The results of both methods were applied to a real data set that indicates the economic performances of European Union member countries and also, a simulation study was done for different sample sizes and for different numbers of input-output, and the results were examined. For both applications, consistent results were obtained. Spearman’s correlation test is employed to compare the rankings obtained by PCA and DEA.

 Key Words: Principal Component Analysis, Data Envelopment Analysis, Ranking

 

Keywords

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References

• A. Charnes, W.W. Cooper, E. Rhodes, “The efficiency of decision making units”, European Journal of Operational Research, Vol. 2, pp.429-444, 1978.
• R.D. Banker, A. Charnes, W.W. Cooper, “Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, Vol. 30, no. 19, 1078-1092, 1984.
• P. Andersen, N. Petersen, “A procedure for ranking efficient units in Data Envelopment Analysis”, Management Science, Vol. 39, no. 10, pp. 1261-1264, 1993.
• I.M. Premachandra, “A note on DEA vs principal component analysis: An improvement to Joe Zhu’s approach”, European Journal of Operational Research, vol. 132, pp. 553-560, 2001.
• W.W. Cooper, L.M. Seiford, K. Tone, "Data Envelopment Analysis", Kluwer Academic Publishers, Boston USA, 100-175, 2000.
• A. Boussofiane, R.G. Dyson, E. Thanassoulis, "Applied data envelopment analysis", European Journal of Operational Research, Vol. 52, pp. 1-15, 1991.
• D.L. Retzlaff-Roberts, “Relating discriminant analysis and data envelopment analysis to one another”, European Journal of Operational Research , Vol. 23, pp. 311-322, 1996.
• N. Adler, L. Friedman, Z. Sinuany-Stern, “Review of ranking methods in the data envelopment analysis context”, European Journal of Operational Research, Vol. 140, pp. 249–265, 2002.
• H. Tatlıdil, “Uygulamalı Çok Değişkenli İstatistiksel Analiz”, Cem Web Ofset, Ankara, 1996.
• J. Zhu, “Data Envelopment Analysis vs principal component analysis: An illustrative study of economic performance of Chinese cities”, European Journal of Operational Research, Vol. 111, pp. 50-61, 1998.
• www.foreigntrade.gov.tr.
• H. Gamgam, “Parametrik Olmayan İstatistiksel Teknikler”, Gazi Üniversitesi Yayınları, Ankara, 1998.