Interval Efficiency Assessment in Network Structure Based on Cross –Efficiency

Subject Areas : policy making

nasim  roudabr ¹ (department of industrial engineering, science and research branch of Islamic Azad university, Tehran)
seyed esmaeil  najafi ² (Department of Industrial Engineering, Tehran Science and Research Branch, Islamic Azad University, Tehran, Iran.)

Received: 2019-03-12 Accepted : 2019-03-12 Published : 2018-03-01

Keywords: * data envelopment analysis, * network DEA, * cross efficiency, * Interval data,

Abstract :

As we know, in evaluating of DMUs some of them might be efficient, so ranking of them have a high significant. One of the ranking methods is cross-efficiency. Cross efficiency evaluation in data envelopment analysis (DEA) is a commonly used skill for ranking decision making units (DMUs). Since, many studies ignore the intra-organizational communication and consider DMUs as a black box. For significant of this subject, we applied cross-efficiency for network DMUs. However, In view of the fact that precise input and output data may not always be available in real world due to the existence of uncertainty, we have developed the model with interval data. the existing classical interval DEA method is not able to rank the DMUs, but can only classify them as efficient or inefficient , so this paper improve that. The proposed method can be used for each network that includes DMUs with two stages in production process. However, this paper is the first study that examined cross efficiency of DMUs in structure framework with interval data. the new approach enables us to ranking of first stage for n DMU and second stages of them. DMUs with the best rank can be used as benchmark for improving efficiency of other DMUs. Finally, We present Illustrate example with two steps for proposed model that can be develop for more than two steps.

References:

References

 

1. Cook, W. D., Liang, L., Zha, Y., & Zhu, J. (2009). A modified super-efficiency DEA model for infeasibility. Journal of the Operational Research Society, 60(2), 276-281.


2. Thanassoulis, E., Kortelainen, M., Johnes, G., & Johnes, J. (2011). Costs and efficiency of higher education institutions in England: a DEA analysis. Journal of the operational research society, 62(7), 1282-1297.


3. Cook, W. D., Harrison, J., Imanirad, R., Rouse, P., & Zhu, J. (2013). Data envelopment analysis with nonhomogeneous DMUs. Operations Research, 61(3), 666-676.


4. Yang, M., Li, Y., Chen, Y., & Liang, L. (2014). An equilibrium efficiency frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs. European Journal of Operational Research, 239(2), 479-489.


5. Imanirad, R., Cook, W. D., Aviles-Sacoto, S. V., & Zhu, J. (2015). Partial input to output impacts in DEA: The case of DMU-specific impacts. European Journal of Operational Research, 244(3), 837-844.


6. Wang, Y. M., & Chin, K. S. (2010). Some alternative models for DEA cross-efficiency evaluation. International Journal of Production Economics, 128(1), 332-338.


7. Ghasemi, M. R., Ignatius, J., & Emrouznejad, A. (2014). A bi-objective weighted model for improving the discrimination power in MCDEA. European Journal of Operational Research, 233(3), 640-650.


8. Charnes, A., Cooper, W., Lewin, A. Y., & Seiford, L. M. (1997). Data envelopment analysis theory, methodology and applications. Journal of the Operational Research society, 48(3), 332-333.


9. Mitropoulos, P., Talias, Μ. A., & Mitropoulos, I. (2015). Combining stochastic DEA with Bayesian analysis to obtain statistical properties of the efficiency scores: An application to Greek public hospitals. European Journal of Operational Research, 243(1), 302-311.


10. Wang, K., Huang, W., Wu, J., & Liu, Y. N. (2014). Efficiency measures of the Chinese commercial banking system using an additive two-stage DEA. Omega, 44, 5-20.


11. Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the operational research society, 45(5), 567-578.


12. Anderson, T. R., Hollingsworth, K., & Inman, L. (2002). The fixed weighting nature of a cross-evaluation model. Journal of Productivity Analysis, 17(3), 249-255.


13. Boussofiane, A., Dyson, R. G., & Thanassoulis, E. (1991). Applied data envelopment analysis. European Journal of Operational Research, 52(1), 1-15.


14. Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: Critique and extensions. New Directions for Program Evaluation, 1986(32), 73-105.


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


16. Shang, J., & Sueyoshi, T. (1995). A unified framework for the selection of a flexible manufacturing system. European Journal of Operational Research, 85(2), 297-315.


17. Sun, S. (2002). Assessing computer numerical control machines using data envelopment analysis. International Journal of Production Research, 40(9), 2011-2039.


18. Ertay, T., & Ruan, D. (2005). Data envelopment analysis based decision model for optimal operator allocation in CMS. European Journal of Operational Research, 164(3), 800-810.


19. Wu, J., Liang, L., & Chen, Y. (2009). DEA game cross-efficiency approach to Olympic rankings. Omega, 37(4), 909-918.


20. Falagario, M., Sciancalepore, F., Costantino, N., & Pietroforte, R. (2012). Using a DEA-cross efficiency approach in public procurement tenders. European Journal of Operational Research, 218(2), 523-529.


21. Lim, S., Oh, K. W., & Zhu, J. (2014). Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market. European Journal of Operational Research, 236(1), 361-368.


22. Cui, Q., & Li, Y. (2015). Evaluating energy efficiency for airlines: An application of VFB-DEA. Journal of Air Transport Management, 44, 34-41.


23. Despotis, D. K. (2002). Improving the discriminating power of DEA: focus on globally efficient units. Journal of the Operational Research Society, 53(3), 314-323.


24. Jahanshahloo, G. R., Lotfi, F. H., Jafari, Y., & Maddahi, R. (2011). Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation. Applied Mathematical Modelling, 35(1), 544-549.


25. Wu, J., Sun, J., & Liang, L. (2012). Cross efficiency evaluation method based on weight-balanced data envelopment analysis model. Computers & Industrial Engineering, 63(2), 513-519.


26. Contreras, I. (2012). Optimizing the rank position of the DMU as secondary goal in DEA cross-evaluation. Applied Mathematical Modelling, 36(6), 2642-2648.


27. Lim, S. (2012). Minimax and maximin formulations of cross-efficiency in DEA. Computers & Industrial Engineering, 62(3), 726-731.


28. Maddahi, R., Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., & Ebrahimnejad, A. (2014). Optimising proportional weights as a secondary goal in DEA cross-efficiency evaluation. International Journal of Operational Research, 19(2), 234-245.


29. Liang, L., Wu, J., Cook, W. D., & Zhu, J. (2008). The DEA game cross-efficiency model and its Nash equilibrium. Operations research, 56(5), 1278-1288.


30. Wu, J., Liang, L., & Yang, F. (2009). Determination of the weights for the ultimate cross efficiency using Shapley value in cooperative game. Expert Systems with Applications, 36(1), 872-876.


31. Wu, J., Sun, J., Song, M., & Liang, L. (2013). A ranking method for DMUs with interval data based on dea cross-efficiency evaluation and TOPSIS. Journal of systems science and systems engineering, 22(2), 191-201.


32. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444.