The Generalized Returns to Scale for Multiplicative Models in Data Envelopment Analysis
محورهای موضوعی : مجله بین المللی ریاضیات صنعتیA. Davoodi 1 , M. Zarepisheh 2 , R. Fallah Nejad 3
1 - Department of Mathematics, Neyshabur Branch, Islamic Azad Universty, Neyshabur, Iran.
2 - Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, USA.
3 - Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran.
کلید واژه: Generalized returns to scale, Multiplicative models, Data Envelopment Analysis, Most Productive Scale Size,
چکیده مقاله :
Generalized Returns To Scale has been introduced to compute the rate of variation in outputs to the variation in inputs up to the Most Productive Scale Size pattern. In this paper, we address the generalized RTS in the multiplicative models and we propose an algorithm to calculate the rate of variations in different intervals. We also demonstrate that the non-discretionary factors can be easily taken into account in the algorithm.
در مدل های متعارفی تحلیل پوششی داده ها، مفهوم بازده به مقیاس براساس نسبت متناسب تغییرات خروجی به نسبت تغییرات ورودی به صورت موضعی تعریف می شود. بازده به مقیاس تعمیم یافته به منظور محاسبه نرخ تغییرات خروجی ها به ورودی ها تا رسیدن به الگوی بیشترین اندازه مقیاس بهره وری تعریف می شود. مدلهای ضربی در تحلیل پوششی داده ها مدلهایی هستند که در آنها به جای اصل تحدب در اصول مجموعه امکان تولید، از اصل تحدب هندسی استفاده می شود. در این مقاله روشی را برای تعیین بازده به مقیاس تعمیم یافته برای مدل های ضربی تحلیل پوششی داده ها معرفی کرده و روی مثالی به صورت عددی آن را بررسی خواهیم نمود. علاوه بر آن نشان خواهیم داد چگونه می توان شاخص های غیرقابل کنترل را که تغییرات در آنها در اختیار تصمیم گیرنده نیست، در مدل لحاظ نمود.
[1] M. Allahyar, M. Rostamy-Malkhalifeh, An Improved Approach for Estimating Returns to Scale in DEA,Bulltain of Malaysian Mathematical Science Society 37 (2014) 1185-1194.
[2] M. Allahyar, M. Rostamy-Malkhalifeh, Negative data in data envelopment analysis: Efficiency analysis and estimating returns to scale, Computers and Industrial Engineering 82 (2015) 78-81.
[3] K. B. Atici, V. V. Podinovski, Mixed partial elasticities in constant returns-to-scale production technologies, European Journal of Operations Research 220 (2012) 262-269.
[4] R. D. Banker, I. Bardhan, W. W. Cooper, A note on returns to scale in DEA, European Journal of Operations Research 88 (1996) 583-585.
[5] R. D. Banker, A. Charnes, W. W. Cooper, A. P. Schinnar, Bi-External principle for frontier estimation and efficiency evaluations, Management Sciince 27 (1981) 1370-1382.
[6] R. D. Banker, A. Charnes, W. W. Cooper, Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis, Management Science 30 (1984) 1078-1092.
[7] R. D. Banker, W. W. Cooper, L. M. Seiford, RM. Thrall, J. Zhu, Returns to scale in different DEA models, European Journal of Operational Research 154 (2004) 345-362.
[8] R. D. Banker, A. Maindiratta, Piecewise loglinear estimation of efficient production sur AR. faces, Management Sciences 32 (1986) 126-135.
[9] M. S. Bazaraa, J. J. Jarvis, H. D. Sherali, Linear Programming and Network Flows, Wiley, (2009).
[10] J. P. Boussemart, W. Briec, N. Peypoch, C. Tavra, α-Returns to scale and multi-output production technologies, European Journal of Operational Research 197 (2009) 332-339.
[11] A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research 2 (1978) 429-444.
[12] A. Charnes, W. W. Cooper, L, Seiford, J. Stutz, Invariant multiplicative efficiency and piecewise cobb-douglas envelopments, Operations Research Letters 2 (1983) 101-103.
[13] A. Charnes, W. W. Cooper, L, Seiford, J. Stutz, A multiplicative model for efficiency analysis, Socioecon Planning Science 16 (1982) 223-224.
[14] W. W. Cooper, L. Seiford, J. Zhu, Data envelopment analysis: History, models, and interpretations, International Series in Operations Research and Management Science 164 (2011) 1-39.
[15] J. Ding, C. Feng, H. Wu, A radial framework for estimating the efficiency and returns to scale of a multi-component production system in DEA, International Series in Operations Research and Management Science 239 (2016) 351-384.
[16] R. Eslami, M. Khoveyni, Right and left returns to scales in data envelopment analysis: Determining type and measuring value, Computers and Industrial Engineering 65 (2013) 500-508.
[17] P. Hadjicostas, A. C. Soteriou, One-sided elasticities and technical efficiency in multioutput production: A theoretical framework, European Journal of Operational Research 168 (2006) 425-449.
[18] M. Mirbolouki, M. Allahyar, A parameterfree approach for estimating the quality and quantity of the right and left returns to scale in Data Envelopment Analysis, Expert Systems with Applications 125 (2019) 170-180.
[19] M. Mu, J. Paradi, J. Ruggiero, Z. Yang, Evaluating alternative DEA models used to control for non-discretionary inputs, Computers and Operations Research 33 (2006) 1173-1183.
[20] M. Omidi, M. Rostamy-Malkhalifeh, A. Payan, F. Hosseinzadeh Lotfi, Estimation of Overall Returns to Scale (RTS) of a Frontier Unit Using the Left and Right RTS, Computational Economist 53 (2019) 633-655.
[21] V. V. Podinovski, F. R. Frsund, V. E. Krivonozhko, A simple derivation of scale elasticity in data envelopment analysis, European Journal of Operational Research 197 (2009) 149-153.
[22] V. V. Podinovski, F. R. Frsund, Differential characteristics of efficient frontiers in data envelopment analysis, Operations Research 58 (2010) 1743-1754.
[23] V. V. Podinovski, R. G. Chambers, K. B. Atici, I. D. Deineko, Marginal values and returns to scale for nonparametric production frontiers, Operations Research 64 (2016) 236-250.
[24] V. V. Podinovski, Returns to scale in convex production technologies, European Journal of Operational Research 258 (2017) 970-982.
[25] J. Ruggiero, Non-discretionary inputs in data envelopment analysis, European Journal of Operational Research 111 (1998) 461-469.
[26] B. K. Sahoo, M. Khoveyni, R. Eslami, P. Chaudhury, Returns to scale and most productive scale size in DEA with negative data, European Journal of Operational Research 255 (2016) 545-558.
[27] M. J. Syrjnen, Non-discretionary and discretionary factors and scale in data envelopment analysis, European Journal of Operational Research 158 (2004) 20-33.
[28] M. Taleb, R. Khalid, R. Ramli, Estimating the return to scale of an integer-valued data envelopment analysis model: efficiency assessment of a higher education institution, Arabian Journal of Basic Application Science 26 (2019) 144-152.
[29] G. L. Yang, W. Liu, Estimating directional returns to scale in DEA, Information science 55 (2017) 243-273.
[30] G. L. Yang, R. Rousseau, L. Yang, W. Liu, A study on directional returns to scale, Journal of Informetr 8 (2014) 628-641.
[31] M. Zarepisheh, M. Soleimani-damaneh, L. Pourkarimi, Determination of returns to scale by CCR formulation without chasing down alternative optimal solutions, Applied Mathematical Letters 19 (2006) 964-967.
[32] M. Zarepisheh, M. Soleimani-damaneh, Global variation of outputs with respect to the variation of inputs in performance analysis; generalized RTS, European Journal of Operational Research 186 (2008) 786-800.
[33] M. Zarepisheh, E. Khorram, G. R. Jahanshahloo, Returns to scale in multiplicative models in data envelopment analysis, Annals of Operational Research 173 (2010) 195-206.
[34] V. Zelenyuk, A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation, European Journal of Operational Research 228 (2013) 592-60
