Returns to scale in decision-making units with integer-valued or mixed inputs and integer-valued or real outputs using radial models in data envelopment analysis

Tavassoli, Zeinab; Rostami-MalKhalifeh, Mohsen; Hosseinzadeh Lotfi, Farhad; AllahVieanloo, Tofigh

doi:10.22105/dmor.2023.347569.1622

Document Type : Original Article

Authors

Department of Applied Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

https://doi.org/10.22105/dmor.2023.347569.1622

Abstract

Purpose: The current paper tries to determine the type of returns to scale in a decision-making unit under the condition that integer-valued inputs or outputs are present.
Methodology: This paper introduces radial models for determining the value and type of Returns to Scale (RTS) in 4 scenarios, including single integer-valued input – single real output (scenario one), mixed inputs – exclusively real outputs (scenario two), exclusively integer-valued inputs – exclusively real outputs (scenario three), and exclusively integer-valued inputs – exclusively integer-valued outputs (scenario four); in each scenario, the values of the left RTS and right RTS are determined, and the RTS type is then determined on that basis. Finally, by presenting three examples based on two scenarios, namely single integer-valued input – single real output and single integer-valued input – single integer-valued output, the new method is compared with previous methods using GAMS software, and the conclusions are provided.
Findings: The type of returns to scale differs when integer-valued inputs or outputs are present as compared with the case where the inputs and outputs are assumed to have real values.
Originality/Value: This study focuses on the value and type of returns to scale for integer-valued data. For this purpose, returns to scale was modeled in 4 scenarios using input-oriented radial models, and in the fourth scenario (exclusively integer-valued inputs – exclusively integer-valued outputs), the modeling was carried out for output orientation as well. The existence of a difference between the results produced by our proposed model and those of the classical model was demonstrated through two examples, one using hypothetical data and the other real-world data.

Keywords

Main Subjects

Data Envelopment Analyses

References

[1] Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429–444.

[2] Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078–1092.

[3] Edalatpanah, S. A., Godarzi Karim, R., Khalilian, B., & Partouvi, S. (2020). Data envelopment analysis and efficiency of firms: a goal programing approach. Innovation management and operational strategies, 1(1), 1-16.

[4] Banker, R. D. (1984). Estimating most productive scale size using data envelopment analysis. European journal of operational research, 17(1), 35–44.

[5] 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.

[6] Banker, R. D., Cooper, W. W., Seiford, L. M., Thrall, R. M., & Zhu, J. (2004). Returns to scale in different DEA models. European journal of operational research, 154(2), 345–362.

[7] Golany, B., & Yu, G. (1997). Estimating returns to scale in DEA. European journal of operational research, 103(1), 28–37.

[8] Fukuyama, H. (2000). Returns to scale and scale elasticity in data envelopment analysis. European journal of operational research, 125(1), 93–112.

[9] Jahanshahloo, G. R., Lotfi, F. H., & Zohrehbandian, M. (2005). Finding the efficiency score and RTS characteristic of DMUs by means of identifying the efficient frontier in DEA. Applied mathematics and computation, 170(2), 985–993.

[10] Allahyar, M., & Rostamy-Malkhalifeh, M. (2014). An Improved Approach for Estimating Returns to Scale in DEA. Bulletin of the malaysian mathematical sciences society, 37, 1185–1194.

[11] Allahyar, M., & Rostamy-Malkhalifeh, M. (2015). Negative data in data envelopment analysis: Efficiency analysis and estimating returns to scale. Computers \& industrial engineering, 82, 78–81.

[12] Omidi, M., Rostamy-Malkhalifeh, M., Payan, A., & Hosseinzadeh Lotfi, F. (2017). Determining Left and right Returns to Scale (RTS) and RTS sustainability by using linear programming problems based on simultaneous changes in inputs and outputs. Journal of new researches in mathematics, 3(11), 59–80.

[13] Daneshvar, S., & Adesina, K. A. (2018). Modified variable return to scale back-propagation neural network robust parameter optimization procedure for multi-quality processes. Engineering optimization, 51(8), 1352–1369.

[14] Saleh, H., Hosseinzadeh, F., Rostamy, M., & Shafiee, M. (2020). Performance evaluation and specifying of Return to scale in network DEA. Journal of advanced mathematical modeling, 10(2), 309–340.

[15] Qamar, A., Ashfaq, M., & Khan, M. T. I. (2017). Resource use efficiency and return to scale analysis in off-season cucumber production in Punjab, Pakistan. Sarhad journal of agriculture, 33(1), 47–52.

[16] Situmorang, J. W. (2018). A review input factors elasticity and return to scale of cooperative: a survey on Indonesian savings-loan cooperatives. Independent journal of management \& production, 9(4), 1274–1290.

[17] Czyżewski, B., Smedzik-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://www.sciencedirect.com/science/article/pii/S0195925520300561

[18] Lozano, S., & Villa, G. (2006). Data envelopment analysis of integer-valued inputs and outputs. Computers \& operations research, 33(10), 3004–3014.

[19] Kuosmanen, T., & Matin, R. K. (2009). Theory of integer-valued data envelopment analysis. European journal of operational research, 192(2), 658–667.

[20] Matin, R. K., & Kuosmanen, T. (2009). Theory of integer-valued data envelopment analysis under alternative returns to scale axioms. Omega, 37(5), 988–995.

[21] Khezrimotlagh, D., Salleh, S., & Mohsenpour, Z. (2012). A comment on theory of integer-valued data envelopment analysis. Applied mathematical sciences, 6(116), 5769–5774.

[22] Khezrimotlagh, D. (2015). Differences between real and integer production possibility sets in data envelopment analysis. ArXiv preprint arxiv:1501.07401.

[23] Zhou, Z., Guo, X., Wu, H., & Yu, J. (2018). Evaluating air quality in China based on daily data: Application of integer data envelopment analysis. Journal of cleaner production, 198, 304–311.

[24] Ren, J., Chen, C., & Gao, B. (2020). Additive integer-valued DEA models with fuzzy undesirable outputs: closest benchmarking targets and super-efficiency. IEEE access, 8, 124857–124868. DOI:10.1109/ACCESS.2020.3007837

[25] Chen, C., Liu, H., Tang, L., & Ren, J. (2021). A range adjusted measure of super-efficiency in integer-valued data envelopment analysis with undesirable outputs. Journal of systems science and information, 9(4), 378–398.

[26] Hosseini Monfared, S. N., Hosseinzadeh Lotfi, F., Mozaffari, M. R., & Rostamy Malkhalifeh, M. (2021). Classifying flexible and integer data in two-stage network data envelopment analysis. Journal of applied research on industrial engineering, 8(3), 270–289.

[27] Taleb, M., Khalid, R., & Ramli, R. (2019). Estimating the return to scale of an integer-valued data envelopment analysis model: efficiency assessment of a higher education institution. Arab journal of basic and applied sciences, 26(1), 144–152.

[28] Taleb, M., Khalid, R., Ramli, R., Ghasemi, M. R., & Ignatius, J. (2022). An integrated bi-objective data envelopment analysis model for measuring returns to scale. European journal of operational research, 296(3), 967–979.

[29] Chandra, P., Cooper, W. W., Li, S., & Rahman, A. (1998). Using DEA to evaluate 29 Canadian textile companies—considering returns to scale. International journal of production economics, 54(2), 129–141.

Journal of Decisions and Operations Research

Returns to scale in decision-making units with integer-valued or mixed inputs and integer-valued or real outputs using radial models in data envelopment analysis

References

References

Volume 8, Issue 3
September 2023
Pages 814-831

Returns to scale in decision-making units with integer-valued or mixed inputs and integer-valued or real outputs using radial models in data envelopment analysis

References

References

Volume 8, Issue 3September 2023Pages 814-831

Volume 8, Issue 3
September 2023
Pages 814-831