Choosing weights for a complete ranking of DMUs in DEA and cross-evaluation

Iranian Journal of Optimization

مقاله 3، دوره 10، شماره 2، اسفند 2018، صفحه 93-99   

نوع مقاله: Research Paper

نویسنده

Parichehr Zamani^*

Faculty of engineering, Qom Branch, Islamic Azad University, Qom, Iran

چکیده

Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. However, DEA does not provide more information about the efficient DMUs. One of the interesting research subjects is to discriminate between efficient DMUs. The aim of this paper is ranking all efficient (extreme and non-extreme) DMUs based on defining the new index which is obtained from basic definitions of models. The proposed method has been able to remove the existing deficiencies in some ranking methods and therefore makes a new contribution to DEA ranking.

کلیدواژه‌ها

Data envelopment analysis؛ Ranking؛ Pure profit؛ cross-efficiency

مراجع

Alirezaee, M. R., & Afsharian, M. (2007). A complete ranking of DMUs using restrictions in DEA models, Applied Mathematics and Computation, 189(2), 1550-1559.

 Amirteimoori, A. R., & Kordrostami, S. (2005). Efficient surfaces and an efficiency index in DEA: A constant returns to scale. Applied Mathematics and Computation, 163(2), 683-691.

Andersen, P., & Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39(10), 1261–1264.

Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional. Naval Research Logistics Quarterly, 9(3-4), 181-186. 

 Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444.

Cooper, W. W., Ruiz, J. L., & Sirvent, I. (2007). Choosing weights from alternative optimal solutions of dual multiplier models in DEA. European Journal of Operational Research, 180(1), 443-458.

Cooper, W. W., Ruiz, J. L., & Sirvent, I. (2009). Selecting non–zero weights to evaluate effectiveness of basketball   players with DEA. European Journal of Operational Research, 195(2), 563-574.

Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations meanings and uses. The Journal of the Operational Research Society, 45(5), 567-578.

Green, R., Doyle, J., & Cook, W. D. (1996). Preference voting and project ranking using DEA and cross-evaluation. European Journal of Operational Research, 90(3), 461-472.

Jahanshahloo, G. R., Junior, H. V., Hosseinzadeh Lotfi, F., & Akbarian, D. (2007). A new DEA ranking system based on changing the reference set. European Journal of Operational Research, 181(1), 331-337.

Jahanshahloo, G. R., Sadeghi. J., & khodabakhshi, M. (2017). Fair ranking of the decision making units using optimistic and pessimistic weights in data envelopment analysis. Rairo-Operations research, 51(1), 253-260.

Khodabakhshi, M., & Aryavash, K. (2012). Ranking all units in data envelopment analysis. Applied mathematics letters, 25(12), 2066-2070.

Liang, L., Wu, J., Cook, W. D., & Zhu, J. (2008). Alternative secondary goals in DEA cross-efficiency evaluation. International Journal of Production Economics, 113(2),1025-1030.

Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: Critique and extensions, in: R.H. Silkman (Ed.), Measuring Efficiency: An Assessment of Data Envelopment Analysis, Wiley, San Francisco.

Wu, J., Liang, L., Zha, Y., & Yang, F. (2009). Determination of cross-efficiency under the principle of rank priority in cross-evaluation. Expert Systems with Applications, 36(3), 4826-4829.

Ziari. M., & Ziari, S. (2016). Ranking efficient DMUs using the variation coefficient of weights in DEA. Iranian Journal of Optimization, 8(1), 897-907.

Ziari. S., & Sharifzadeh, M. (2017). An approach to rank efficient DMUs in DEA based on combining manhattan and Infinity Norms. Iranian Journal of Optimization, 9(1),13-19.