The way to deal with flexible data from their stochastic presence point of view as output or input in the evaluation of efficiency of the decision-making units (DMUs) motivates new perspectives in modeling and solving data envelopment analysis (DEA) in the presence of flexible variables. Because the orientation of flexible data is not pre-determined, and because the number of DMUs is fixed and all the DMUs are independent, flexible data can be treated as random variable in terms of both input and output selection. As a result, the selection of flexible variable as input or output for n DMUs can be regarded as binary random variable. Assuming the randomness of choosing flexible data as input or output, we deal with DEA models in the presence of flexible data whose input or output orientation determines a binomial distribution function. This study provides a new insight to classify flexible variable and investigates the input or output status of a variable using a stochastic model. The proposed model obviates the problems caused by the use of the large M number and using its different values in previous models. In addition, it can obtain the most appropriate efficiency value for decision-making units by assigning the chance of choosing the orientation of flexible variable to the model itself. The proposed method is compared with other available methods by employing numerical and empirical examples.
Mansour Sharifi, Ghasem Tohidi, Behrouz Daneshian, Farzin Modarres Khiyabani
. A New Stochastic Model for Classifying Flexible Measures in Data Envelopment Analysis[J]. Journal of the Operations Research Society of China, 2021
, 9(3)
: 569
-592
.
DOI: 10.1007/s40305-020-00318-5
[1] Charnes, A., Cooper, W.W., Rhodes, E.:Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2, 429-444(1978)
[2] Banker, R.D.:Estimating most productive scale size using data envelopment analysis. Eur. J. Oper. Res. 17, 35-44(1984)
[3] Charnes, A., Cooper, W.W.:Chance-constrained programming. Manag. Sci. 15, 73-79(1959)
[4] Azizi, H., Amirteimoori, A.:Classifying inputs and outputs in interval data envelopment analysis. J. Ind. Syst. Eng. 10(2), 134-150(2017)
[5] Huang, Z., Li, S.X.:Dominance stochastic models in data envelopment analysis. Eur. J. Oper. Res. 95(2), 390-403(1996)
[6] Cooper, W.W., Deng, H., Huang, Z., Li, S.X.:Chance constrained programming approaches to congestion in stochastic data envelopment analysis. Eur. J. Oper. Res. 155(2), 487-501(2004)
[7] Khodabakhshi, M., Asgharian, M.:An input relaxation measure of efficiency in stochastic data envelopment analysis. Appl. Math. Model. 33, 2010-2023(2009)
[8] Cook, W.D., Zhu, J.:Classifying inputs and outputs in DEA. Eur. J. Oper. Res. 180, 692-699(2007)
[9] Toloo, M.:On classifying inputs and outputs in DEA:a revised model. Eur. J. Oper. Res. 198, 358-360(2009)
[10] Amirteimoori, A., Emrouznejad, A.:Flexible measures in production process:a DEA-based approach. RAIRO Oper. Res. 25, 63-74(2011)
[11] Tohidi, G., Matroud, F.:A new non-oriented model for classifying flexible measures in DEA. J. Oper. Res. Soc. 68, 1019-1029(2017)
[12] Azizi, H., Amirteimoori, A.:Classifying inputs and outputs in interval data envelopment analysis. J. Ind. Syst. Eng. 10(2), 134-150(2017)
[13] Amirteimoori, A., Emrouznejad, A., Khoshandam, L.:Classifying flexible measures in data envelopment analysis:a slack-based measure. Measurement 46, 4100-4107(2013)
[14] Martin, B.:Classifying flexible measures in data envelopment analysis:a slacks-based measure-a comment. Measurement 150, 107045(2020)
[15] Ashrafi,A.,Jaafar,A.B.,Lee,L.S.:OnclassifyinginputsandoutputsinDEA:arevisedmodel.Institute for Mathematical Research, vol. 1. University Putra Malaysia, 43400 UPM Serdang, Selangor (2011)
[16] Vasant, P., Zelinka, I., Weber, G.:Intelligent Computing and Optimization. Springer, Cham (2018)
[17] Vasant, P., Zelinka, I., Weber, G.:Intelligent computing and optimization. In:Proceedings of the 2nd International Conference on Intelligent Computing and Optimization 2019, Springer International Publishing, ISBN:978-3-030-33585-4
[18] Thomas, J., Karagoz, P., Bazeer, A.B., Vasant, P.:Intelligent Computing and Optimization. Springer, Cham (2019)
[19] Ganesan, T., Vasant, P., Sanghvi, P., Joshua Thomas, J., Litvinchev, I.:Random matrix generators for optimizing a fuzzy biofuel supply chain system. J. Adv. Eng. Comput. 4, 33-50(2020)
[20] Thomas, J.J., Karagoz, P., Bazeer, A.B, Vasant, P.:Deep Learning Techniques and Optimization Strategies in Big Data Analytics. IGI Global, Nov 29, 2019-Computers, 355 pp (2019). https://doi.org/10.4018/978-1-7998-1192-3
