رتبهبندی واحدهای تصمیمگیرنده با استفاده از کارایی متقاطع در حضور خروجیهای نامطلوب و عدم قطعیت دادهها
محورهای موضوعی : آمار
1 - 1) گروه مدیریت، مرکز تحقیق در عملیات و اقتصاد، دانشگاه کاتولیک لوون، لوون لنو، بلژیک
2) گروه ریاضی، واحد اردبیل، دانشگاه آزاد اسلامی، اردبیل، ایران
کلید واژه: Data Envelopment Analysis, Cross efficiency, Ranking, Uncertainty, Undesirable outputs,
چکیده مقاله :
کارایی متقاطع یک ابزار سودمند برای رتبهبندی واحدهای تصمیمگیرنده (DMU) در تحلیل پوششی دادها (DEA) میباشد. اما از انجا که ممکن است در ارزیابی DMUها وزنهای بهینه منحصر بفرد نباشد لذا انتخاب یکی از آنها کار سادهای نخواهد بود و ممکن است نتایج حاصل از جوابهای بهینه دگرین، متفاوت باشد. برای این منظور، در این مقاله، روشی برای رتبه بندی DMUها که مشکل غیر یکتایی را ندارد، ارایه میشود. از آنجا که خروجیها به دوصورت مطلوب و نامطلوب به کار میروند. پس ارایه مدلهایی برای رتبهبندی واحدهای تصمیمگیرنده در حضور خروجیهای مطلوب ونامطلوب حایز اهمیت است. ازطرفی مدلهای DEA کلاسیک بادادههای قطعی سروکار دارد. ولی دردنیای واقعی، لزوماً همه دادهها قطعی نمیباشند. در نتیجه، به دنبال رویکردی هستیم که کارایی DMU را در شرایط عدم قطعیت محاسبه کند. لذا واحدهای تصمیمگیرنده باخروجیهای مطلوب ونا مطلوب بازهای رتبهبندی میشوند. برای رویارویی با این مسئله، یک کران پایین و یک کران بالا برای کارایی براساس رویکرد بازهای پیشنهاد میشود. نتایج حاصل در یک مثال عددی ساده مورد تحلیل قرار میگیرد.
Cross efficiency is one of the useful methods for ranking of decision making units (DMUs) in data envelopment analysis (DEA). Since the optimal solutions of inputs and outputs weights are not unique so the selection of them are not simple and the ranks of DMUs can be changed by the difference weights. Thus, in this paper, we introduce a method for ranking of DMUs which does not have a unique problem. In the real life, the outputs can be shown as desirable and undesirable outputs. So it is important to provide models for the ranking of DMUs in present of desirable and undesirable outputs. The classic DEA models deals with certain data. But, in the real word, all data are not necessarily certain. For solve of this problem, we present a new method that compute the ranks of all DMUs by uncertain data and calculate the lower and upper bounds for the ranks of DMUs. Finally, the results of a simple example are given.
[1] Aghayi, N, Tavana, M., Raayatpanah, .A., (2016), Robust efficiency measurement with common set of weights under varying degrees of conservatism and data uncertainty, European Journal Industrial Engineering, 10, 385-405.
[2] Aghayi, N. (2016) Revenue Efficiency Measurement with Undesirable Data in Fuzzy DEA. Proceedings of the7th International Conference on Intelligent Systems, Modelling and Simulation, publisher IEEE, Thailand.
[3] Aghayi, N. (2017). Cost efficiency measurement with fuzzy data in DEA. Journal of Intelligent and Fuzzy Systems, 32, 409–420 .
[4] Aghayi, N., Maleki, B., (2016). Efficiency Measurement of DMUs with Undesirable outputs under uncertainty based on the directional distance function: Application on Bank Industry. Energy, 112, 376-387.
[5] Andersen, P., Petersen, N.C., (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39 (10), 1261-1264.
[6] Caves, D. W., Christensen, L. R., Diewert, E., (1982). Multilateral comparisons of output, input and productivity using superlative index numbers. The Economic Journal, 92 (365), 73-86.
[7] Chambers, R. G., Chung, Y., Fare, R., (1996). Benefit and distance function. Journal of Economic Theory, 70 (2), 407-419.
[8] Charnes, A., Cooper, W. W., Rhodes, E., (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2 (6), 429-444.
[9] Chen, Y., Du, J., Huo, J., (2013). Super-efficiency based on a modified directional distance function. Omega, 41 (3), 621-625.
[10] Chung, Y. H., Fare, R., Grosskopf, S., (1997). Productivity and undesirable outputs a directional distance function approach. Journal of Environmental Management, 51 (3), 229-240.
[11] Cook, W., Roll, Y., Kazakov, A., (1990). DEA model for measuring the relative efficiencies of highway maintenance patrols. INFOR 28 (2), 811-818.
[12] Dimitrov, Stanko and Sutton, Warren, (2013), Generalized symmetric weight assignment technique: Incorporating managerial preferences in data envelopment analysis using a penalty function, Omega, 41(1), 48 – 54.
[13] Dong, G., (2013). A complete ranking of DMUs with undesirable outputs restrictions in DEA models. Mathematical and Computer Modelling, 58 (5-6), 1102-1109.
[14] Doyle, J.R., Green, R.H., (1994). Efficiency and cross-efficiency in DEA: derivations, meanings and uses. Journal of the Operational Research Society, 45 (5), 567-578.
[15] Emrouznejad, A., Rostamy-Malkhalifeh, M., Hatami-Marbini, A., Tavana, M., Aghayi, N., (2011). An overall profit Malmquist productivity
index with fuzzy and interval data. Mathematical and Computer Modelling, 54 (11-12), 2827-2838.
[16] Hosseinzadeh Lotfi, F., Hatami-Marbini, A., Agrell, Per J., Aghayi, N., Gholami, K., (2013). Allocating fixed resources and setting targets using a common-weights DEA approach. Computers & Industrial Engineering 64, (2), 631-640.
[17] Hosseinzadeh Lotfi, F., Rostamy-Malkhalifeh, M., Aghayi, N., Ghelej Beigi, Z., Gholami, K., (2013). An improved method for ranking alternatives in multiple criteria decision analysis. Applied Mathematical Modelling, 37, (1-2), 25-33.
[18] Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Jafari, Y., Maddahi, R., (2011). Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation, Applied Mathematical Modelling 35 (1), 544-549
[19] Kao, C., Hung, H.T., (2005). Data envelopment analysis with common weights: the compromise solution approach. Journal of the Operational Research Society 56 (10), 1196-1203.
[20] Liu, W., Zhongbao, Z., Ma, Ch., Liu, D., Shen, W., (2015). Two-stage DEA models with undesirable input intermediate-outputs. Omega, 56, 74-87.
[21] Liu, X., Chu, J., Yin, P., Sun, J., (2016), DEA cross-efficiency evaluation considering undesirable output and ranking priority: a case study of eco-efficiency analysis of coal-fired power plants, Journal of Cleaner Production, 142 (2), 1-9.
[22] Pittman, R. W., (1983). Multilateral productivity comparisons with undesirable outputs. Economic Journal, 93 (372), 883-891.
[23] Rostamy-Malkhalifeh, M., Aghayi, N. (2011). Two Ranking of Units on the Overall Profit Efficiency with Interval Data. Mathematics Scientific Journal, 8(2), 73–93.
[24] Rostamy-Malkhalifeh, M., Aghayi, N., (2011) Measuring overall profit efficiency with fuzzy data. Journal of Mathematical Extension, 5 (2), 73-90.
[25] Ruiz, J.L., Sirvent, I., (2012). On the DEA total weight flexibility and the aggregation in cross-efficiency evaluations. European Journal of Operational Research 223 (3), 732-738.
[26] Saffar Ardabili, J., Aghayi, N., Monzali., (2007). New efficiency using undesirable factors of data envelopment analysis. Modeling & Optimization, 9 (2), 249-255.
[27] Salehpour,S., Aghayi, N., (2015). The Most Revenue Efficiency with Price Uncertainty. International Journal of Data Envelopment Analysis, 3, 575-592.
[28] Seiford, L. M., Zhu, J., (2002). Modeling undesirable factors inefficiency valuation. European Journal of Operational Research, 142 (1), 16-20.
[29] Sexton, T.R., Silkman, R.H., 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, CA, 73-105.
[30] Sueyoshi, T., (1999). DEA non-parametric ranking test and index measurement: slackadjusted DEA and an application to Japanese agriculture cooperatives. Omega Int. J. Management Science 27 (3), 315-326.
[31] Sun, J., Wu, J., Guo, D., (2013). Performance ranking of units considering ideal and anti-ideal DMU with common weights. Applied Mathematical Modelling, 37 (9), 6301-6310.
[32] Toloo, M., Aghayi, N., Rostamy- Malkhalifeh, M., (2008). Measuring overall profit efficiency with interval data. Applied Mathematics and Computation, 201 (1-2), 640-649.
[33] Wang, Y. M., Chin, K. S, (2010). A neutral DEA model for cross-efficiency evaluation and its extension, Expert Systems with Applications 37, 3666-3675.
[34] Wang, Y.M., Chin, K.S., Wang, S., (2012). DEA models for minimizing weight disparity in cross-efficiency evaluation. Journal of the Operational Research Society, 63 (8), 1079-1088.
[35] Wang, Y.M., Greatbanks, R., Yang, B. (2005), Interval Efficiency Assessment Using Data Envelopment Analysis; Fuzzy Sets and Systems 153, 347–370
[36] Wanke, P., Barros, C. P., Emrouznejad, A., (2016). Assessing productive efficiency of banks using integrated Fuzzy-DEA and bootstrapping a case of Mozambican banks. European Journal of Operational Research, 249(1), 378-389.
[37] Wu, J., Chu, J., Sun, J., Zhu, Q., (2016). DEA cross-efficiency evaluation based on Pareto improvement. European Journal of Operational Research 248 (2), 571-579.
[38] Zhu, J., (1999). Infeasibility of super-efficiency data envelopment analysis models. INFOR 37 (2), 174-187