Document Type : Research Paper
Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran.
Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran.
We extend the concept of returns to scale in Data Envelopment Analysis (DEA) to the weight restriction environments. By adding weight restrictions, the status of returns to scale, i.e. increasing, constant, and decreasing, may need a change. We first define "returns to scale" underweight restrictions and propose a method for identifying the status of returns to scale. Then, we demonstrated that this addition would usually narrow the region of the most productive scale size (MPSS). Finally, for an inefficient decision-making unit (DMU), we will present a simple rule for determining the status of returns to the scale of its projected DMU. Here, we carry out an empirical study to compare the proposed method's results with the BCC model. In addition, we demonstrate the change in the MPSS for both models. We have presented different models of DEA to determine returns to scale. Here, we suggested a model that determines the whole status to scale in decision-making units.
Different models of DEA to determine returns to scale are presented. Here, we suggested a model that determines the whole status to scale in decision-making units.
- Abri, A. G. (2013). An investigation on the sensitivity and stability radius of returns to scale and efficiency in data envelopment analysis. Applied mathematical modelling, 37(4), 1872-1883. https://doi.org/10.1016/j.apm.2012.04.047
- Alirezaee, M., Hajinezhad, E., & Paradi, J. C. (2018). Objective identification of technological returns to scale for data envelopment analysis models. European journal of operational research, 266(2), 678-688. https://doi.org/10.1016/j.ejor.2017.10.016
- Banker, R. D., & Thrall, R. M. (1992). Estimation of returns to scale using data envelopment analysis. European journal of operational research, 62(1), 74-84. https://doi.org/10.1016/0377-2217(92)90178-C
- Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444. https://doi.org/10.1016/0377-2217(78)90138-8
- Czyżewski, B., Smędzik-Ambroży, K., & Mrówczyńska-Kamińska, A. (2020). Impact of environmental policy on eco-efficiency in country districts in Poland: How does the decreasing return to scale change perspectives? Environmental impact assessment review, 84, 106431. https://doi.org/10.1016/j.eiar.2020.106431
- Bernstein, D. H. (2020). An updated assessment of technical efficiency and returns to scale for US electric power plants. Energy policy, 147, 111896. https://doi.org/10.1016/j.enpol.2020.111896
- Eslami, R., & Khoveyni, M. (2013). Right and left returns to scales in data envelopment analysis: Determining type and measuring value. Computers & industrial engineering, 65(3), 500-508. https://doi.org/10.1016/j.cie.2013.02.012
- Hatami-Marbini, A., Beigi, Z. G., Hougaard, J. L., & Gholami, K. (2018). Measurement of returns-to-scale using interval data envelopment analysis models. Computers & industrial engineering, 117, 94-107. https://doi.org/10.1016/j.cie.2017.12.023
- Ghasemi, S., Aghsami, A., & Rabbani, M. (2020). Data envelopment analysis for estimate efficiency and ranking operating rooms: a case study. International journal of research in industrial engineering, 10(1), 67-86. DOI: 22105/riej.2021.247705.1143
- Khodadadi, M., & Zare Haghighi, H. (2017). Two methods for measuring the environmental returns to scale using data envelopment analysis approach. Iranian journal of management studies, 10(2), 499-526. DOI: 22059/IJMS.2017.227335.672527
- Mirbolouki, M., & Allahyar, M. (2019). A parameter-free approach for estimating the quality and quantity of the right and left returns to scale in data envelopment analysis. Expert systems with applications, 125, 170-180. https://doi.org/10.1016/j.eswa.2019.01.065
- Monzeli, A., Daneshian, B., Tohidi, G., Sanei, M., & Razavian, S. (2020). Efficiency study with undesirable inputs and outputs in DEA. Journal of fuzzy extension and applications, 1(1), 76-84. DOI: 22105/jfea.2020.248018.1005
- Montazeri, F. Z. (2020). An overview of data envelopment analysis models in fuzzy stochastic environments. Journal of fuzzy extension and applications, 1(4), 291-299. DOI: 22105/jfea. 2020.258330.1030
- Nayebi, M., & Hosseinzadeh Lotfi, F. (2016). The methods of ranking based super efficiency. International journal of research in industrial engineering, 5(1 (4)), 43-66. DOI: 22105/RIEJ.2017.49169
- Kohl, S., & Brunner, J. O. (2020). Benchmarking the benchmarks–comparing the accuracy of data envelopment analysis models in constant returns to scale settings. European journal of operational research, 285(3), 1042-1057. https://doi.org/10.1016/j.ejor.2020.02.031
- Taeb, Z., Hosseinzadeh Lotfi, F., & Abbasbandy, S. (2017). Determine the efficiency of time depended units by using data envelopment analysis. International journal of research in industrial engineering, 6(3), 193-201. https://dx.doi.org/10.22105/riej.2017.49156
- Reddy, T. (2015). Comparison and Correlation Coefficient between CRS and VRS models of OC Mines. International journal of ethics in engineering & management education, 2(1), 2348-4748.
- Toloo, M., & Allahyar, M. (2018). A simplification generalized returns to scale approach for selecting performance measures in data envelopment analysis. Measurement, 121, 327-334. https://doi.org/10.1016/j.measurement.2018.02.056
- Sueyoshi, T., & Wang, D. (2017). Measuring scale efficiency and returns to scale on large commercial rooftop photovoltaic systems in California. Energy economics, 65, 389-398. https://doi.org/10.1016/j.eneco.2017.04.019