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Ranking decision making units with the integration of the multi-dimensional scaling algorithm into PCA-DEA

Yıl 2017, Cilt: 46 Sayı: 6, 1187 - 1197, 01.12.2017

Mehmet Guray Unsal H. Hasan Orkcu

Öz

Data envelopment analysis (DEA) has being used commonly in a variety of fields since it was developed, and its development continues through interacting with other techniques. Since the method can be applied to multiple inputs and outputs, it interacts with multivariate statistical methods. Principle component analysis (PCA) is a multivariate analysis method used to destroy the independence structure between variables or to reduce the number of dimensions. In literature, PCA and DEA are compared for ranking decision making units. Then, PCA-DEA procedure was modified. In this study, the multidimensional scaling (MDS) algorithm, which is one of the commonly used methods in multivariate statistics, is integrated to the PCA-DEA method to rank the decision making units (DMUs). According to Spearman rank correlation, the proposed method gives a higher correlation with super efficiency compared to other methods.

Anahtar Kelimeler

Data envelopment analysis ranking problem multivariate statistics principle component analysis multi-dimensional scaling

Kaynakça

  • Charnes A., Cooper W.W., Rhodes E. Measuring the efficiency of decision making units, Eur. J. Oper. Res. 2, 429-444, 1978.
  • Banker R.D., Charnes A., Cooper W.W. Some models for estimating technical and scale inefficiencies in data envelopment analysis, Manage. Sci. 30 (19), 1078-1092, 1984.
  • Andersen P., Petersen N. A procedure for ranking efficient units in data envelopment analysis, Manage. Sci. 39 (10), 1261-1264, 1993.
  • Sexton T.R., Silkman R.H., Hogan A.J. Data envelopment analysis: Critique and Extensions. In: Silkman, R.H. (Ed.), Measuring Efficiency: An assessment of data envelopment analysis., Jossey-Bass, San Francisco , 73-105, 1986.
  • Podinovski V.V., Athanassopoulos A. Assessing the relative efficiency of decision making units in DEA models with weight restrictions, J. Oper. Res. Soc. 49, 500-508, 1998.
  • Meza L.A., Lins M.P.E. Review of methods for increasing discrimination in data envelopment analysis, Ann. Oper. Res. 116, 225-242, 2002.
  • Sun S., Lu W.M. A cross-efficiency profiling for increasing discrimination in data envelopment analysis, INFOR 43 (1), 51-60, 2005.
  • Jahanshahloo G. R., Memariani A., Hosseinzadeh L.F., Shoja N. A feasibel interval for weights in data envelopment analysis, Appl. Math. Comput. 160, 155-168, 2005.
  • Jahanshahloo G.R., Hosseinzadeh L.F., Jafari Y., Maddahi R. Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation, Appl. Math. Model. 35, 544-549, 2011.
  • Alirezaee M.R., Afsharian M.A. A complete ranking of DMUs using restrictions in DEA models, Appl. Math. Comput. 189, 1550-1559, 2007.
  • Orkcu H.H., Bal H. Goal programming approaches for data envelopment analysis cross efficiency evaluation, Appl. Math. Comput. 218, 346-356, 2011.
  • Hosseinzadeh L.F., Jahanshahloo G.R., Esmaeili M. An alternative approach in the estimation of returns to scale under weight restrictions, Appl. Math. Comput. 189, 719-724, 2007.
  • Wu J., Liang L., Yang F. A modified complete ranking of DMUs using restrictions in DEA models, Appl. Math. Comput. 217, 745-751, 2010.
  • Bal H., Orkcu H.H., Celebioglu S., A new method based on the dispersion of weights in data envelopment analysis, Comput. Ind. Eng. 54 (3), 502-512, 2008.
  • Bal H., Orkcu H.H., Celebioglu S., Improving the discrimination power and weights dispersion in the data envelopment analysis, Comput. Oper. Res. 37 (1), 99-107, 2010.
  • Lam K.F. In the determination weight sets to compute cross-efficiency ratios in DEA, J. Oper. Res. Soc. 61, 134-143, 2010.
  • Cooper W.W., Ruiz J.L., Sirvent I. Choosing weights from alternative optimal solutions of dual multiplier models in DEA, Eur. J. Oper. Res. 180 (1), 243-258, 2007.
  • Wang Y.M., Chin K.S. Some alternative models for DEA cross-efficiency evaluation, Int. J. Prod. Eco. 128 (1), 332-338, 2010.
  • Wang Y.M., Chin K.S., Peng J. Weight determination in the cross-efficiency evaluation, Comput. Ind. Eng. 61, 497-502, 2011.
  • Sinuany-Stern Z., Friedman L. DEA and the discriminant analysis of ratios for ranking units, Eur. J. Oper. Res. 111, 470-478, 1998.
  • Friedman L., Sinuany-Stern Z. Scaling units via the canonical correlation analysis and the DEA, Eur. J. Oper. Res. 100, 629-637, 1997.
  • Johnson R.A., Wichern D.W. Multivariate Statistical Analysis, 5.th Edition, Prentice Hall 2002.
  • Zhu J. Data envelopment analysis vs principal component analysis: An illustrative study of economic performance of Chinese cities, Eur. J. Oper. Res. 111, 50-61, 1998.
  • Premachandra I.M. A note on DEA vs principal component analysis: An improvement to Joe Zhu’s approach, Eur. J. Oper. Res. 132, 553-560, 2001.
  • Rossi F., Tomas A.A. Analysis of the beverage data using cluster analysis, rotated principal components analysis and LOESS curves, Food Qual. Prefer. 12, 437-445, 2001.
  • Azadeh A., Amalnick M.S., Ghaderi S.F., Asadzadeh S.M. An integrated DEA PCA numerical taxonomy approach for energy efficiency assessment and consumption optimization in energy intensive manufacturing sectors, Energy Policy 35, 3792-3806, 2007.
  • Retzlaff-Roberts D.L. Relating discriminant analysis and data envelopment analysis to one another, Eur. J. Oper. Res. 23, 311-322, 1996.
  • Adler N., Friedman L., Sinuany-Stern Z. Review of ranking methods in the data envelopment analysis context, Eur. J. Oper. Res. 140, 249-265, 2002.
  • Kardiyen, F., Orkcu H.H. Comparison of Principal Component Analysis and Data Envelopment Analysis in Ranking of Decision Making Units, G.U. Journal of Science 19, (2) 127-133, 2006.
  • http://www.dpt.gov.tr/bgyu/bgyu.html.
  • Giraleas, D., Emrouznejad, A., Thanassoulis, E. Productivity change using growth accounting and frontier-based approaches - Evidence from a Monte Carlo analysis, Eur. J. Oper. Res. 222, 673-683, 2012.

Yıl 2017, Cilt: 46 Sayı: 6, 1187 - 1197, 01.12.2017

Mehmet Guray Unsal H. Hasan Orkcu

Öz

Kaynakça

  • Charnes A., Cooper W.W., Rhodes E. Measuring the efficiency of decision making units, Eur. J. Oper. Res. 2, 429-444, 1978.
  • Banker R.D., Charnes A., Cooper W.W. Some models for estimating technical and scale inefficiencies in data envelopment analysis, Manage. Sci. 30 (19), 1078-1092, 1984.
  • Andersen P., Petersen N. A procedure for ranking efficient units in data envelopment analysis, Manage. Sci. 39 (10), 1261-1264, 1993.
  • Sexton T.R., Silkman R.H., Hogan A.J. Data envelopment analysis: Critique and Extensions. In: Silkman, R.H. (Ed.), Measuring Efficiency: An assessment of data envelopment analysis., Jossey-Bass, San Francisco , 73-105, 1986.
  • Podinovski V.V., Athanassopoulos A. Assessing the relative efficiency of decision making units in DEA models with weight restrictions, J. Oper. Res. Soc. 49, 500-508, 1998.
  • Meza L.A., Lins M.P.E. Review of methods for increasing discrimination in data envelopment analysis, Ann. Oper. Res. 116, 225-242, 2002.
  • Sun S., Lu W.M. A cross-efficiency profiling for increasing discrimination in data envelopment analysis, INFOR 43 (1), 51-60, 2005.
  • Jahanshahloo G. R., Memariani A., Hosseinzadeh L.F., Shoja N. A feasibel interval for weights in data envelopment analysis, Appl. Math. Comput. 160, 155-168, 2005.
  • Jahanshahloo G.R., Hosseinzadeh L.F., Jafari Y., Maddahi R. Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation, Appl. Math. Model. 35, 544-549, 2011.
  • Alirezaee M.R., Afsharian M.A. A complete ranking of DMUs using restrictions in DEA models, Appl. Math. Comput. 189, 1550-1559, 2007.
  • Orkcu H.H., Bal H. Goal programming approaches for data envelopment analysis cross efficiency evaluation, Appl. Math. Comput. 218, 346-356, 2011.
  • Hosseinzadeh L.F., Jahanshahloo G.R., Esmaeili M. An alternative approach in the estimation of returns to scale under weight restrictions, Appl. Math. Comput. 189, 719-724, 2007.
  • Wu J., Liang L., Yang F. A modified complete ranking of DMUs using restrictions in DEA models, Appl. Math. Comput. 217, 745-751, 2010.
  • Bal H., Orkcu H.H., Celebioglu S., A new method based on the dispersion of weights in data envelopment analysis, Comput. Ind. Eng. 54 (3), 502-512, 2008.
  • Bal H., Orkcu H.H., Celebioglu S., Improving the discrimination power and weights dispersion in the data envelopment analysis, Comput. Oper. Res. 37 (1), 99-107, 2010.
  • Lam K.F. In the determination weight sets to compute cross-efficiency ratios in DEA, J. Oper. Res. Soc. 61, 134-143, 2010.
  • Cooper W.W., Ruiz J.L., Sirvent I. Choosing weights from alternative optimal solutions of dual multiplier models in DEA, Eur. J. Oper. Res. 180 (1), 243-258, 2007.
  • Wang Y.M., Chin K.S. Some alternative models for DEA cross-efficiency evaluation, Int. J. Prod. Eco. 128 (1), 332-338, 2010.
  • Wang Y.M., Chin K.S., Peng J. Weight determination in the cross-efficiency evaluation, Comput. Ind. Eng. 61, 497-502, 2011.
  • Sinuany-Stern Z., Friedman L. DEA and the discriminant analysis of ratios for ranking units, Eur. J. Oper. Res. 111, 470-478, 1998.
  • Friedman L., Sinuany-Stern Z. Scaling units via the canonical correlation analysis and the DEA, Eur. J. Oper. Res. 100, 629-637, 1997.
  • Johnson R.A., Wichern D.W. Multivariate Statistical Analysis, 5.th Edition, Prentice Hall 2002.
  • Zhu J. Data envelopment analysis vs principal component analysis: An illustrative study of economic performance of Chinese cities, Eur. J. Oper. Res. 111, 50-61, 1998.
  • Premachandra I.M. A note on DEA vs principal component analysis: An improvement to Joe Zhu’s approach, Eur. J. Oper. Res. 132, 553-560, 2001.
  • Rossi F., Tomas A.A. Analysis of the beverage data using cluster analysis, rotated principal components analysis and LOESS curves, Food Qual. Prefer. 12, 437-445, 2001.
  • Azadeh A., Amalnick M.S., Ghaderi S.F., Asadzadeh S.M. An integrated DEA PCA numerical taxonomy approach for energy efficiency assessment and consumption optimization in energy intensive manufacturing sectors, Energy Policy 35, 3792-3806, 2007.
  • Retzlaff-Roberts D.L. Relating discriminant analysis and data envelopment analysis to one another, Eur. J. Oper. Res. 23, 311-322, 1996.
  • Adler N., Friedman L., Sinuany-Stern Z. Review of ranking methods in the data envelopment analysis context, Eur. J. Oper. Res. 140, 249-265, 2002.
  • Kardiyen, F., Orkcu H.H. Comparison of Principal Component Analysis and Data Envelopment Analysis in Ranking of Decision Making Units, G.U. Journal of Science 19, (2) 127-133, 2006.
  • http://www.dpt.gov.tr/bgyu/bgyu.html.
  • Giraleas, D., Emrouznejad, A., Thanassoulis, E. Productivity change using growth accounting and frontier-based approaches - Evidence from a Monte Carlo analysis, Eur. J. Oper. Res. 222, 673-683, 2012.
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm İstatistik
Yazarlar

Mehmet Guray Unsal

H. Hasan Orkcu

Yayımlanma Tarihi 1 Aralık 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 46 Sayı: 6

Kaynak Göster

APA Unsal, M. G., & Orkcu, H. H. (2017). Ranking decision making units with the integration of the multi-dimensional scaling algorithm into PCA-DEA. Hacettepe Journal of Mathematics and Statistics, 46(6), 1187-1197.
AMA Unsal MG, Orkcu HH. Ranking decision making units with the integration of the multi-dimensional scaling algorithm into PCA-DEA. Hacettepe Journal of Mathematics and Statistics. Aralık 2017;46(6):1187-1197.
Chicago Unsal, Mehmet Guray, ve H. Hasan Orkcu. “Ranking Decision Making Units With the Integration of the Multi-Dimensional Scaling Algorithm into PCA-DEA”. Hacettepe Journal of Mathematics and Statistics 46, sy. 6 (Aralık 2017): 1187-97.
EndNote Unsal MG, Orkcu HH (01 Aralık 2017) Ranking decision making units with the integration of the multi-dimensional scaling algorithm into PCA-DEA. Hacettepe Journal of Mathematics and Statistics 46 6 1187–1197.
IEEE M. G. Unsal ve H. H. Orkcu, “Ranking decision making units with the integration of the multi-dimensional scaling algorithm into PCA-DEA”, Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 6, ss. 1187–1197, 2017.
ISNAD Unsal, Mehmet Guray - Orkcu, H. Hasan. “Ranking Decision Making Units With the Integration of the Multi-Dimensional Scaling Algorithm into PCA-DEA”. Hacettepe Journal of Mathematics and Statistics 46/6 (Aralık 2017), 1187-1197.
JAMA Unsal MG, Orkcu HH. Ranking decision making units with the integration of the multi-dimensional scaling algorithm into PCA-DEA. Hacettepe Journal of Mathematics and Statistics. 2017;46:1187–1197.
MLA Unsal, Mehmet Guray ve H. Hasan Orkcu. “Ranking Decision Making Units With the Integration of the Multi-Dimensional Scaling Algorithm into PCA-DEA”. Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 6, 2017, ss. 1187-9.
Vancouver Unsal MG, Orkcu HH. Ranking decision making units with the integration of the multi-dimensional scaling algorithm into PCA-DEA. Hacettepe Journal of Mathematics and Statistics. 2017;46(6):1187-9.

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