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A Goal Programming Approach to Weight Dispersion in Data Envelopment Analysis

Year 2007, Volume: 20 Issue: 4, 117 - 125, 28.03.2010

Abstract

In this study, a multi-criteria data envelopment analysis (MCDEA) model, used in the literature to moderate the homogeneity of weights dispersion, is solved using pre-emptive goal programming. The MCDEA model solved using pre-emptive goal programming gives the same relative efficiency as the classical DEA model while it improves the homogeneity of input-output weights. This conclusion is confirmed by the computational results obtained when the two models are applied to a real data set relative to the socio-economic performances of European countries and to randomly generated instances with various numbers of decision making units, inputs and outputs.

 

References

  • Charnes, A., Cooper, W.W., Rhodes, E., “Measuring The Efficiency of Decision Making Units”, European Journal of Operational Research, 2, 429- , (1978).
  • Meza, L.A., Lins, M.P.E., “Review of Methods for Increasing Discrimination in Data Envelopment Analysis”, Annals of Operations Research, 116, 242, (2002).
  • Thompson, R.G., Singleton, F.G., Thrall, R.M., Smith, B.A., ”Comparative Site Evaluations for Locating a High-Energy Physics Lab in Texas”, Interfaces, 16: 35-49, (1986).
  • Thompson, R.G., Langemeier, L.N., Lee, C.T., Thrall, R.M., “The Role of Multiplier Bounds in Efficiency Analysis with Application to Kansas Farming”, Journal of Econometrics, 46: 93-108 (1990).
  • Charnes, A., Cooper, W.W, Huang, Z.M., Sun, D.B., “Polyhedral Cone-Ratio Models with an Illustrative Application to Large Commercial Banks”, Journal of Econometrics, 46: 73-91 (1990).
  • Wong, Y.H.B, Beasley, J.E., “Restricting Weight Flexibility in Data Envelopment Analysis”, Journal of the Operational Research Society, 41(9): 829-835 (1990).
  • Zhu, J., “Data Envelopment Analysis with Preference Structure”, Journal of the Operational Research Society, 47, 136-150 (1996).
  • Halme, M., Joro, T., Korhonen, P., Salo, S., Wallenius, J., “A Value Efficiency Approach to Incorporating Preference Information in Data Envelopment Analysis”, Management Science, 45, 115, (1999).
  • Jahanshahloo, G.R., Memariani, A., Hosseinzadeh, F., Shoja, N., “A Feasible Interval for Weights in Data Envelopment Analysis”, Applied Mathematics and Computation, 160, 155-168, (2005).
  • Allen, R., Athanassopoulos, A., Dyson, R.G., Thanassoulis, E., “Weight Restrictions and Value Judgement in Data Envelopment Analysis: Evolution, Development and Future Directions”, Annals of Operations Research, 73, 13-34, (1997).
  • Podinovski, V.V., Athanassopoulos, A., “Assessing the Relative Efficiency of Decision Making Units in DEA Models with Weight Restrictions”, Journal of the Operational Research Society, 49, 500-508 (1998).
  • Podinovski, V.V., “Computation Efficient Targets in DEA Models with Production Trade-offs and Weight Restrictions”, European Journal of Operational Research, 181, 586-591, (2007).
  • Cooper, W.W., Ruiz, J.L., Sirvent I., "Choosing Weights from Alternative Optimal Solutions of Dual Multiplier Models in DEA", European Journal of Operational Research, 180, 443-458, (2007).
  • Kousmanen, T., Cherchye, L., Sipilainen, T., “The Law of One Price in Data Envelopment Analysis: Restricting Weight Flexibility Across Firms”, European Journal of Operational Research, 170, 757 (2006).
  • Cooper, W.W., Seiford, L.M., Tone, K., "Data Envelopment Analysis", Kluwer Academic Publishers, Boston, USA (2000).
  • Li, X.B., Reeves, G.R., “A multiple criteria approach to data envelopment analysis”, European Journal of Operational Research, 115: 507-517 (1999).
  • Zeleny, M., “Multiple Criteria Decision Making”, McGraw-Hill, New York, USA, 215-280 (1982).
  • Ignizio, J.P., “Goal Programming and Extension”, Lexington Books, Lexington, 20-55 (1976).
  • Bal, H., Örkcü, H.H., Çelebioğlu, S., “An Experimental Comparison of the new Goal Programming and the Linear Programming Approaches in the Two-Group Discriminant Problems”, Engineering, 50 (3): 296-311 (2006).
  • DPT(Devlet Planlama Teşkilatı- Turkish Republic Prime Ministry State Planning Organization) , AB Üyesi Ülkelerde ve Aday Ülkelerde Ekonomik Gelişmeler, AB ile İlişkiler Genel Müdürlüğü, Şubat 2007, http://www.dpt.gov.tr/abigm/abmeg/2007ekonomi k gelisme.pdf.
Year 2007, Volume: 20 Issue: 4, 117 - 125, 28.03.2010

Abstract

References

  • Charnes, A., Cooper, W.W., Rhodes, E., “Measuring The Efficiency of Decision Making Units”, European Journal of Operational Research, 2, 429- , (1978).
  • Meza, L.A., Lins, M.P.E., “Review of Methods for Increasing Discrimination in Data Envelopment Analysis”, Annals of Operations Research, 116, 242, (2002).
  • Thompson, R.G., Singleton, F.G., Thrall, R.M., Smith, B.A., ”Comparative Site Evaluations for Locating a High-Energy Physics Lab in Texas”, Interfaces, 16: 35-49, (1986).
  • Thompson, R.G., Langemeier, L.N., Lee, C.T., Thrall, R.M., “The Role of Multiplier Bounds in Efficiency Analysis with Application to Kansas Farming”, Journal of Econometrics, 46: 93-108 (1990).
  • Charnes, A., Cooper, W.W, Huang, Z.M., Sun, D.B., “Polyhedral Cone-Ratio Models with an Illustrative Application to Large Commercial Banks”, Journal of Econometrics, 46: 73-91 (1990).
  • Wong, Y.H.B, Beasley, J.E., “Restricting Weight Flexibility in Data Envelopment Analysis”, Journal of the Operational Research Society, 41(9): 829-835 (1990).
  • Zhu, J., “Data Envelopment Analysis with Preference Structure”, Journal of the Operational Research Society, 47, 136-150 (1996).
  • Halme, M., Joro, T., Korhonen, P., Salo, S., Wallenius, J., “A Value Efficiency Approach to Incorporating Preference Information in Data Envelopment Analysis”, Management Science, 45, 115, (1999).
  • Jahanshahloo, G.R., Memariani, A., Hosseinzadeh, F., Shoja, N., “A Feasible Interval for Weights in Data Envelopment Analysis”, Applied Mathematics and Computation, 160, 155-168, (2005).
  • Allen, R., Athanassopoulos, A., Dyson, R.G., Thanassoulis, E., “Weight Restrictions and Value Judgement in Data Envelopment Analysis: Evolution, Development and Future Directions”, Annals of Operations Research, 73, 13-34, (1997).
  • Podinovski, V.V., Athanassopoulos, A., “Assessing the Relative Efficiency of Decision Making Units in DEA Models with Weight Restrictions”, Journal of the Operational Research Society, 49, 500-508 (1998).
  • Podinovski, V.V., “Computation Efficient Targets in DEA Models with Production Trade-offs and Weight Restrictions”, European Journal of Operational Research, 181, 586-591, (2007).
  • Cooper, W.W., Ruiz, J.L., Sirvent I., "Choosing Weights from Alternative Optimal Solutions of Dual Multiplier Models in DEA", European Journal of Operational Research, 180, 443-458, (2007).
  • Kousmanen, T., Cherchye, L., Sipilainen, T., “The Law of One Price in Data Envelopment Analysis: Restricting Weight Flexibility Across Firms”, European Journal of Operational Research, 170, 757 (2006).
  • Cooper, W.W., Seiford, L.M., Tone, K., "Data Envelopment Analysis", Kluwer Academic Publishers, Boston, USA (2000).
  • Li, X.B., Reeves, G.R., “A multiple criteria approach to data envelopment analysis”, European Journal of Operational Research, 115: 507-517 (1999).
  • Zeleny, M., “Multiple Criteria Decision Making”, McGraw-Hill, New York, USA, 215-280 (1982).
  • Ignizio, J.P., “Goal Programming and Extension”, Lexington Books, Lexington, 20-55 (1976).
  • Bal, H., Örkcü, H.H., Çelebioğlu, S., “An Experimental Comparison of the new Goal Programming and the Linear Programming Approaches in the Two-Group Discriminant Problems”, Engineering, 50 (3): 296-311 (2006).
  • DPT(Devlet Planlama Teşkilatı- Turkish Republic Prime Ministry State Planning Organization) , AB Üyesi Ülkelerde ve Aday Ülkelerde Ekonomik Gelişmeler, AB ile İlişkiler Genel Müdürlüğü, Şubat 2007, http://www.dpt.gov.tr/abigm/abmeg/2007ekonomi k gelisme.pdf.
There are 20 citations in total.

Details

Primary Language English
Journal Section Statistics
Authors

Hasan Bal This is me

H. Hasan Örkçü

Publication Date March 28, 2010
Published in Issue Year 2007 Volume: 20 Issue: 4

Cite

APA Bal, H., & Örkçü, H. H. (2010). A Goal Programming Approach to Weight Dispersion in Data Envelopment Analysis. Gazi University Journal of Science, 20(4), 117-125.
AMA Bal H, Örkçü HH. A Goal Programming Approach to Weight Dispersion in Data Envelopment Analysis. Gazi University Journal of Science. March 2010;20(4):117-125.
Chicago Bal, Hasan, and H. Hasan Örkçü. “A Goal Programming Approach to Weight Dispersion in Data Envelopment Analysis”. Gazi University Journal of Science 20, no. 4 (March 2010): 117-25.
EndNote Bal H, Örkçü HH (March 1, 2010) A Goal Programming Approach to Weight Dispersion in Data Envelopment Analysis. Gazi University Journal of Science 20 4 117–125.
IEEE H. Bal and H. H. Örkçü, “A Goal Programming Approach to Weight Dispersion in Data Envelopment Analysis”, Gazi University Journal of Science, vol. 20, no. 4, pp. 117–125, 2010.
ISNAD Bal, Hasan - Örkçü, H. Hasan. “A Goal Programming Approach to Weight Dispersion in Data Envelopment Analysis”. Gazi University Journal of Science 20/4 (March 2010), 117-125.
JAMA Bal H, Örkçü HH. A Goal Programming Approach to Weight Dispersion in Data Envelopment Analysis. Gazi University Journal of Science. 2010;20:117–125.
MLA Bal, Hasan and H. Hasan Örkçü. “A Goal Programming Approach to Weight Dispersion in Data Envelopment Analysis”. Gazi University Journal of Science, vol. 20, no. 4, 2010, pp. 117-25.
Vancouver Bal H, Örkçü HH. A Goal Programming Approach to Weight Dispersion in Data Envelopment Analysis. Gazi University Journal of Science. 2010;20(4):117-25.