کاهش تفاوت بین پروفایل وزن ها در کارایی متقاطع تصادفی
محورهای موضوعی : آمارسمیه رحمانی 1 , محسن خون سیاوش 2 , رضا کاظمی متین 3 , زهره مقدس 4
1 - گروه ریاضی، واحد قزوین، دانشگاه آزاد اسلامی، قزوین، ایران
2 - گروه ریاضی، واحد قزوین، دانشگاه آزاد اسلامی، قزوین، ایران
3 - گروه ریاضی، واحد کرج، دانشگاه آزاد اسلامی،کرج، ایران
4 - گروه ریاضی، واحد قزوین، دانشگاه آزاد اسلامی، قزوین، ایران
کلید واژه: difference between the weights, Stochastic cross-efficiency, Cross-efficiency, Data Envelopment Analysis,
چکیده مقاله :
ارزیابی کارایی متقاطع یک رویکرد موثر و در عین حال معمول برای ارزیابی کارایی واحدهای تصمیم گیرنده DMU)) در تحلیل پوششی داده ها (DEA) است. منحصر بفرد نبودن وزن ها در کارایی متقاطع ضعف بزرگی برای این روش قدرتمند است. در این مقاله روش جدیدی در انتخاب پروفایل های وزنی که در ارزیابی کارایی متقاطع تصادفی مورد استفاده قرار می‌گیرند، پیشنهاد داده می شود. یکی از موضوعات اصلی که در اینجا به آن پرداخته می شود دوری از وزن صفر است، زیرا استفاده از وزن صفر دلالت بر این دارد که برخی از متغیرهای مورد نظر از ارزیابی حذف شده‌اند. علاوه بر اجتناب از وزن‌های صفر، انتخاب وزن‌ها طوری انجام می شود که تفاوت بین وزن‌ها را تا جایی که ممکن است کاهش دهد. بنابراین، ایده جدید ارزیابی کارایی متقاطع تصادفی با مجموعه ی وزن های محدود شده در این مقاله است. مدل پیشنهادی، مجموعه مشترکی از وزن‌ها را با استفاده از ایده شباهت بین وزن‌ها استخراج می نماید. از مثالهای عددی برای تشریح روش جدید و مقایسه ی نتایج با روش های دیگر استفاده شده است.
Cross-efficiency method is a useful tool for efficiency evaluation of decision-making units in data envelopment analysis. The issue of non-uniqueness of optimal weights in the cross-efficiency evaluation has reduced the usefulness of this powerful method. This paper introduces a new method for selection of weights profiles as the secondary goal in cross-efficiency with stochastic data. The issue of zero-weight which implies the exclusion of some variables from the assessments, is also addressed in the new proposed method. The provided weights selection method also reduces the weight disparity in the achieved weights profile. In the peer-restricted stochastic cross-efficiency evaluation, the new approach guarantees that different DMUs should not attach very different weights to the same variables. As the result, a common set of weights using the idea of similarity between sets of weights is achieved in the proposed computation method. Some numerical examples are also used for illustration and comparison purposes.
[1] Charnes, A., Cooper, W.W., & Rhodes, E., (1978), Measuring the efficiency of decision making units, European journal of operational Research, 2, 429-444.
[2] Wu, J., Chu, J.F., Sun, J.S., & Zhu, Q.Y., (2016), DEA cross efficiency evaluation based on Pareto improvement, European Journal of Operational Research,248 (2),571-579.
[3] Moeini, M., Karimi, B., and Khorram, E., (2015) Modelling, Computation and Optimization in Information Systems and Management Sciences. Springer International Publishing. 487-498.
[4] Zhou, Z., Lin, L., Xiao, H., Ma, C., Wu, S., (2017), Stochastic network DEA models for two-stage systems under the centralized control organization mechanism, Doi : http://dx.doi.org/10.1016/j.cie.2017.06.005.
[5] Yang, C. C., (2014), An enhanced DEA model for decomposition of technical efficiency in banking, Journal of the Annals of Operations Research,167-185.
[6] Emrouznejad, A., & Yang, G. L., (2018), A survey and analysis of the first 40 years of scholarly literature in DEA, Socio‐Economic Planning Sciences, 61, 4–8.
[7] Liu, S.T., (2018), A DEA ranking method based on cross efficiency intervals and signal-to-noise ratio, Annals of Operations Research, 261(1-2), 207-232.
[8] Sexton, T. R., Silkman, R. H., and Hogan, A. J., (1986), Data envelopment analysis: critique and extensions. In: Silkman R H (Ed.) Measuring Efficiency: An Assessment of data Envelopment Analysis, Jossey-Bass San Francisco, Pp: 73–105.
[9] Anderson, T.R.., Hollings Worth, K.B., & Inman, L. B., (2002), The fixed weighting nature of a cross evaluation model, Journal of Productivity Analysis, 18, 249-255.
[10] Lim, S., and Zhu, J., (2014), DEA cross-efficiency evaluation under variable returns to scale, Journal of the Operational Research Society,1-12.
[11] Cui, Q., & Li, Y., (2015), Evaluating energy efficiency for airlines: an application of VFB-DEA, Journal of Air Transport Management, 44, 34–41.
[12] Doyle, J. R., and Green, R. H., (1994), Efficiency and cross-efficiency in DEA: derivations, meanings and uses, Journal of the Operational Research Society, 45 (5): 567–578.
[13] Cook, W. D., and Zhu, J., (2014), DEA Cobb–Douglas frontier and cross-efficiency, Journal of the Operational Research Society, 65(2): 265–268.
[14] Wu, J., Chu, J.F., Sun, J.S., & Zhu, Q.Y., (2016), DEA cross efficiency evaluation based on Pareto improvement, European Journal of Operational Research,248 (2),571-579.
[15] Liu, S.T., (2018), A DEA ranking method based on cross efficiency intervals and signal-to-noise ratio, Annals of Operations Research, 261(1-2), 207-232.
[16] Kao, C., Liu, S. (2018), Cross efficiency measurement and decomposition in two basic network systems, Omega,1-10.
[17] Wu, J., Chu, J. F., Sun, J. S., Zhu, Q. Y., & Liang, L., (2016), Extended secondary goal models for weights selection in DEA cross-efficiency evaluation, Computers & Industrial Engineering, 93, 143-151.
[18] Ramón, N., Ruiz, J. L., and Sirvent, I., (2010), On the choice of weights profiles in cross efficiency evaluations, European Journal of Operational Research, 207 (3):1564-1572.
[19] Soltanifar, M., Shahghobadi, S., (2013), Selecting a benevolent secondary goal model in data an envelopment analysis cross-efficiency evaluation by a voting, Socio-Economic Planning Sciences,159-167.
[20] Thompson, R. G., Singleton, F. D., Thrall, R. M., and Smith, B. A., (1986), Comparative site evaluations for locating a high-energy physics lab in Texas, Interfaces 16 (6): 35–49.
[21] Ramón, N., Ruiz, J. L., Sirvent, I., (2011), Reducing differences between profiles of weights: A ‘‘peer-restricted’’ cross-efficiency evaluation, Omega, 39 (6): 634–641.
[22] Jahanshahloo, G. R., Hosseinzadeh Lofti, F., Yafari, and Maddahi, R., (2011), Selecting symmetric weights as a secondary goal in DEA cross efficiency evaluation, Applied Mathematical Modelling, 35(1): 544–549.
[23] Wu, J., Chu, J. F., Sun, J. S., Zhu, Q. Y., & Liang, L., (2016), DEA cross-efficiency evaluation based on satisfaction degree: an application to technology, (2016).
[24] Charles, V., Cornillier, F., (2017), Value of the Stochastic Efficiency in Data Envelopment Analysis, Expert Systems With Applications, doi: 10.1016/j.eswa.2017.03.061.
[25] Cooper, W.W., Honghui, D., Huang, Z. & Li, S.X., (2004), Chance constrained programming approaches to congestion in stochastic data envelopment analysis, European Journal of Operational Research,155 (2), 487-501.
[26] Cooper, W.W., Deng, H., Huang, Z., & Li, S.X., (2002), Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis, Journal of the Operational Research Society, 53, 1347–1356.
[27] Khodabakhshi, M., (2009), Estimating most productive scale size with stochastic data in data envelopment analysis, Economic Modelling, doi: 10. 1016.j. econmod.2009.03.002.
[28] Zhou, Z., Lin, L., Xiao, H., Ma, C., Wu, S., (2017), Stochastic network DEA models for two-stage systems under the centralized control organization mechanism, Doi : http://dx.doi.org/10.1016/j.cie.2017.06.005