کشسانی انتخابی در تحلیل پوششی داده ها با حضور خروجی های مطلوب و نامطلوب
محورهای موضوعی : تحقیق در عملیاتمریم حقیقت شناس 1 , علیرضا امیرتیموری 2 , سهراب کردرستمی 3
1 - گروه ریاضی، دانشکده علوم پایه، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران
2 - گروه ریاضی، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران
3 - گروه ریاضی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران
کلید واژه: تحلیل پوششی داده ها, کشسانی مقیاس, کارایی هزینه, خروجی های نامطلوب,
چکیده مقاله :
بازده به مقیاس و کشسانی مقیاس موضوعات مهمی در تحلیل پوششی داده ها به شمار می روند . در کشسانی مقیاس ارزیابی پاسخ بردارهای خروجی نسبت به تغییرات حاشیه ا ی بردارهای ورودی به صورت کمی مورد نظر است . در اغلب فعالیت های تولیدی و اقتصادی علاوه بر خروجی های مطلوب ، خروجی های نامطلوب مانند مطالبات معوق در بانک ها ایجاد می شوند . در این مقاله روی اندازه کشسانی مقیاس انتخابی بر مبنای قیمت داده ها و با حضور خروجی های نامطلوب تمرکز شده است . در اینجا با تغییر جزئی در خروجی های ناطلوب تعیین می شود که بین ورودی ها و خروجی های مطلوب کدام یک به عنوان پاسخ تغییر در خروجی های نامطلوب انتخاب شوند . در انتها برای نمایش کاربرد چارچوب تئوری پیشنهادی، مدل برای داده ها ی واقعی یکی از بانک ها ی استانی در ایران به کار برده شده است .
Returns to scale and scale elasticity are two important issues in data envelopment analysis ( DEA ) . In scale elasticity, the evaluating of the response of output vectors with respect to marginal changes of input vectors in quantitative form is considered . I n the most productive and economic activities, in addition to the desirable outputs, undesirable outputs su ch as deferred loans of banks, is created . In this paper, it is focused on selective scale elasticity based on data p rices in the presence of undesirable outputs . Here with a little change in undesirable outputs, it is interesting to know between inputs and desirable outputs , which one must be changed to have the least cost. In the following, to show the real applicability of the proposed theoretical framework, it is applied to a real case on one of the provincial banks i n Iran .
[1] Banker, R. D., Charnes, A., & Cooper, W.W., 1984. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science. 30, 1078-1092.
[2] Banker, R. D. and R. M. Thrall. (1992). “Estimation of Returns to Scale Using Data Envelopment Analysis.” European Journal of Operational Research 62, 74–84.
[3] Forsund, F.R. and L. Hjalmarsson. (2004). “Are All Scales Optimal in DEA Theory and Empirical Evidence.” Journal of Productivity Analysis, 21, 25–48.
[4] Førsund, F. R., Hjalmarsson, L., Krivonozhko, V. E., & Utkin, O. B., 2007a. Calculation of scale elasticity in DEA models: direct and indirect approaches. Journal of Productivity Analysis 28, 45-56.
[5] Krivonozhko, V .E., Volodin, A.V., Sablin , I.A ., Patrin , M., 2004. Constructions of economic functions and calculation of marginal rates in DEA using parametric optimization methods. Journal of the Operational Research Society 55, 1049–1058.
[6] Førsund, F.R., Kittelsen, S.A.C., Krivonozhko, V.E., 2007b. Farrell revisited: Visualising the DEA production frontier. Memorandum 15/2007, Department of Economics, University of Oslo.
[7] Podinovski, V. V., Førsund, F. R., Krivonozhko, & V. E., 2009. A simple derivation of scale elasticity in data envelopment analysis. European Journal of Operational Research 197, 149–153.
[8] Podinovski, V. V., & Førsund, F. R., 2010. Differential characteristics of efficient frontiers in data envelopment analysis. Operations Research 58, 1743–1754.
[9] Atici, K. B., and Podinovski, V. V., 2012. Mixed partial elasticities in constant returns-to-scale production technologies. European Journal of Operational Research 220, 262-269.
[10] Zelenyuk V., 2013. A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation. European Journal of Operational Research, 228(3), 592-600.
[11] Sahoo B., & Tone K., 2015. Scale Elasticity in Non-parametric DEA Approach. In: Zhu J. (eds) Data Envelopment Analysis. International Series in Operations Research & Management Science, 221. Springer, Boston, MA.
[12] Mirjaberi, M., & Kazemi Matin, R., 2015. Computation of scale elasticity in presence of exogenously fixed inputs. Measurement. 73, 275-283.
[13] Krivonozhko V.E., Førsund F.R., Lychev A.V. (2014) Measurement of returns to scale using non-radial DEA models European Journal of Operational Research 232(3): 664–670.
[14] Krivonozhko, V. E., Lychev, A. V., & Førsund, F. R. (2017). Measurement of returns to scale in radial DEA models. Computational Mathematics and Mathematical Physics, 57(1), 83-93.
[15] Sahoo, B. K., Zhu, J., Tone, K., & Klemen, B. M. (2014). Decomposing technical efficiency and scale elasticity in tow-stage network DEA. European Journal of Operational Research, 233(3), 584-594.
[16] Khaleghi, M., Jahanshahloo, G., Zohrehbandian, M., & Lotfi, F. H. (2012). Returns to scale and scale elasticity in two-stage DEA. Mathematical and computational applications, 17(3), 193-202.
[17] Mirjaberi, M., & Kazemi Matin, R. (2016). On the calculation of directional scale elasticity in data envelopment analysis. Asia-Pacific Journal of Operational Research, 33(04), 1650026.
[18] Amirmohammadi, H., Amirteimoori, A. A., Kordrostami, S., & Vaez-Ghasemi, M. (2021). Scale elasticity in the presence of integer data: An application to electricity distribution companies. Studies of Applied Economics, 39(2).
[19] Amirmohammadi, H., Amirteimoori, A., Kordrostami, S., & Ghasemi, M. V. Scale elasticity in the presence of undesirable and nondiscretionary factors: an application to bank branches. Italian Journal of Pure and Applied Mathematics, 101.
[20] Fathi Ajirlu, S., Amirteimoori, A., & Kordrostami, S., Measuring the cost efficiency in NDEA. Journal of New Researches in Mathematics, 2020, 6(27), 141-154.
[21] Sarab, R. G., Amirteimoori, A., Malek, A., & Kordrostami, S. (2021). Cost efficiency analysis in data envelopment analysis framework: An application to sugar industries. Journal of Information and Optimization Sciences, 42(5), 1137-1161.
[22] Azizi Usefvand, R., Kordrostami, S., Amirteimoori, A., & Daneshmand-Mehr, M. (2022). Estimating the directional scale elasticity of two-stage processes in the presence of undesirable outputs. Modern Research in Decision Making.
[23] Farrell, M. J., 1957. The measurement of productive efficiency. Journal of the royal statistical society. 120, 253-290.
[24] Debreu (1951), The coefficient of resource utilization, Econometrica 19, pp.273-292.
[25] Färe, R., Grosskopf, S.,Lovell, C. A. K., (1985). The measurement of efficiency of production. Kluwer-Nijhoff, Boston.
[26] Cooper, W.W., Seiford, L.M., Tone, K., (2000). Data Envelopment Analysis. Kluwer Academic Publishers, Dordrecht.
[27] Tone, K., Sahoo, B. K. (2006). Re-examining scale elasticity in DEA. Annals of Operations Research, 145, 69-87.
[28] Sahoo, B. K., Tone, K. (2017). Determining returns to scale in the VRS DEA model. Advances in DEA Theory and Applications: With Extensions to Forecasting Models, 33-39.
[29] Hailu, A., Veeman, T. S., (2001). Nonparametric productivity analysis with undesirable outputs: An application to the Canadian pulp and paper industry. American Journal of Agricultural Economics, 85, 1075-1077.
[30] Seiford, L., and Zhu, J., (2002). Models for undesirable factors in efficiency evaluation. European Journal of Operational Research, 142, 16-20.
[31] Färe, R., Grosskopf, S., (2003). Nonparametric productivity analysis with undesirable outputs: comment. American Journal of Agricultural Economics, 85, 1070-1074.
[32] Kuosmanen, T., (2005). Weak disposability in nonparametric production analysis with undesirable outputs. American Journal of Agricultural Economics, 87, 1077-1082.
