An algorithm for determining common weights by concept of membership function

Journal of Linear and Topological Algebra

مقاله 1، دوره 04، شماره 03، آبان 2015، صفحه 165-172   

نوع مقاله: Research Paper

نویسندگان

S. Saati^* ؛ N. Nayebi

Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

چکیده

Data envelopment analysis (DEA) is a method to evaluate the relative efficiency of decision making units (DMUs). In this method, the issue has always been to determine a set of weights for each DMU which often caused many problems. Since the DEA models also have the multi-objective linear programming (MOLP) problems nature, a rational relationship can be established between MOLP and DEA problems to overcome the problem of determining weights. In this study, a membership function was defined base on the results of CCR model and cross efficiency, and by using this membership function in a proposed model, we obtained a common set of weights for all DMUs. Finally, by solving a sample problem, the proposed algorithm was explained.

کلیدواژه‌ها

Data envelopment analysis (DEA)؛ Cross efficiency؛ Membership function؛ Common Set of Weights؛ Multi-objective programming problem

مراجع

[1] A. Charnes, W. W. Cooper, Management models and industrial applications of linear programming, John Wiley, New York, 1961.

[2] A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiency of decision making units, European journal of operational research. (1978), 2, 429-444.

[3] G. R. Jahanshahloo, A. Memariani, F. Hosseinzadeh Lotfi and H. Z. Rezai, A note on some of DEA models and finding efficiency and complete ranking using common set of weights, Applied mathematics and computation. (2005), 166, 265-281.

[4] J. Lu, G. Zhang, D. Ruan and F. Wu, Multi-objective group decision making methods software and applications with fuzzy set techniques. Imperial collage press. 2007.

[5] Y. Roll, W. Cook and B. Golany, Controlling factor weights in data envelopment analysis. IIE Trans, (1991), 23, 2-9.

[6] T. Roll, B. Golany, Alternate methods of treating factor weights in data envelopment analysis, Omega, (1993), 21, 99-109.

[7] M. S. Saati, Determining a common set of weights in DEA by solving a linear programming, Journal of industrial engineering international, (2008), 6, 51-56.

[8] T. R. Sexton, R. H. Silkman and A. J. Hogan, Data envelopment analysis: critique and extensions. In: R.H. Silkman (Ed.), Measuring efficiency: An assessment of data envelopment analysis. San Francisco, CA, Jossey-Bass, 1986.

[9] Y. M. Wang, K. P. Chin, Some alternative models for DEA cross efficiency evaluation, Production economics, (2010), 128, 332-33.

[10] Y. M. Wand, K. S. Chin and Y. Luo, Cross efficiency evaluation based on ideal and anti-ideal decision making units, Expert systems with applications, (2011), 38, 10312-10319.