Determining Left and right Returns to Scale (RTS) and RTS sustainability by using linear programming problems based on simultaneous changes in inputs and outputs

Subject Areas : Statistics

M. Omidi ¹ , M. Rostamy-Malkhalifeh ² , A. Payan ³ , F. Hosseinzadeh Lotfi ⁴

1 - Department of Mathematics, Science and research Branch, Islamic Azad University, Tehran , Iran
2 - Department of Mathematics, Science and research Branch, Islamic Azad University, Tehran , Iran
3 - Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran
4 - Department of Mathematics, Science and research Branch, Islamic Azad University, Tehran , Iran

Received: 2016-12-25 Accepted : 2017-05-08 Published : 2017-10-23

Keywords: تحلیل پوششی داده‌ها (DEA), بازده به مقیاس چپ (L-RTS), بازده به مقیاس راست (R-RTS), بازده به مقیاس کلی (O-RTS), پایداری,

Abstract :

Determining the type of returns to scale (RTS) and identifying stability region for RTS of evaluating unit are appropriate abilities for forecasting the future the unit when its size is changed. This paper aims to introduce RTS sustainability of frontier decision making units (DMUs) in data envelopment analysis (DEA). Based on the importance of RTS in relation to decisions of managers, different methods have been proposed to define RTS and determine the type RTS. Research on RTS led to a more general categorize for the type of RTS, named left RTS (L-RTS) and right RTS (R-RTS). All of the methods in evaluating L-RTS and R-RTS have presented parametric programming problems which are non-linear programs, naturally. In tis situation, researchers are facing the challenge to determine the value of parameters. In order to survey this limitation, the present paper suggests linear programming problems. Moreover, the proposed models with minor changes are appropriate tools for determining the RTS sustainability for evaluating unit.

References:

 

[1] جهانشاهلو، غلامرضا.؛ حسین­زاده لطفی، فرهاد.؛ نیکومرام، هاشم.؛1387. "تحلیل پوششی داده­ها و کاربردهای آن". تهران: انتشارات دانشگاه آزاد اسلامی، واحد علوم تحقیقات.

 

[2] Allahyar, M., Rostamy-Malkhalifeh, M., 2014. An improved approach fore stimating returns to scale in DEA, Bulletin of the Malaysian Mathematical Sciences Society, 2, 37(4), 1185–1194.

 

[3] Banker, R. D., 1984. Estimating most productive scale size using data envelopment analysis, European Journal of Operation Research, 17 35–44.

 

[4] 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.

 

[5] Banker, R. D., Thrall, R. M., 1992. Estimation of Returns to Scale Using Data Envelopment Analysis, European Journal of Operational Research, 62,74–84.

 

[6] Banker, R. D., Chang, H., Cooper, W. W., 1996. Equivalence and implementation of alternative methods for determining returns to scale in data envelopment analysis, European Journal of Operational Research, 89, 473-81.

 

[7] Charnes, A., Cooper, W. W., Rhodes, E., 1978. Measuring the efficiency of decision making units, European Journal of Operation Research, 2, 429-444.

 

[8] Charnes, W.W. Cooper, B. Golany, L. Seiford, J. Stutz, Foundations of data envelopment analysis for pareto-koopmans efficient empirical production functions, J. Econom. 30 (1985) 91–107.

 

[9] Eslami, R., Khoveyni, M., 2013. Right and Left returns to scales in data analysis, Determining type and measuring value, Computers & Industrial Engineering, 15, 500–501.

 

[10] Fare, R., Grosskopf, S., Lovell, CAK., 1994. Production Frontiers. Cambridge University Press.

Golany, B., Yu, G., 1997. Estimating Returns to Scale in DEA, European Journal of Operational Research, 103, 28–37.

 

[11] Hadjicostas, P., Soteriou, A. C. 2006. One-sided elasticities and technical efficiency in multi-output production: a theoretical framework, European Journal of Operational Research, 168 (2), 425–449.

 

[12] Khodabakhshi, M., Gholami,Y., Kheirollahi, H., 2010.  An additive model approach for estimating returns to scale in imprecise data envelopment analysis, Applied Mathematical Modelling, 34, 1247–1257.

 

[13] Omidi, M., Rostamy-Malkhalifeh, M., Payan, A., Hosseinzadeh Lotfi, F., 2017.

 

[14] Estimation of Overall Returns to Scale (RTS) of a Frontier Unit Using the Left and Right RTS, Computational Economics, https://doi.org/10.1007/s10614-017-9756-7.

 

[15] Seiford, L.M., Zhu, J., 1999. An investigation of returns to scale in data envelopment analysis, Omega.

 

[16] Tone, K., Sahoo, B.K., 2004. Degree of scale economies and congestion: A unified DEA approach, European Journal of Operational Research, 158, 755–772.

 

[17] Zhu, Joe., Shen. Shen, Z., 1995. A Discussion of Testing DMUs’ Returns to Scale, European Journal of Operational Research, 81, 590–596.