A Slacks-based Nonlinear DEA Model with Integer Data : an Application to Departments of the Islamic Azad University, Karaj Branch in Iran

• Autorzy: Zahra Moazenzadeh , Saber Saati , Reza Farzipoor Saen , Reza Kazemi Matin , Sevan Sohraee
• Języki publikacji: EN

Abstrakty

EN

Although Data Envelopment Analysis (DEA) assumes that inputs and outputs take non-negative real values, in some realworld cases, data are integer-valued. In some situations, rounding a fractional value to the closest integer can lead to a misleading evaluation of efficiency and in some cases may lead to an infeasible projection point. To date, various radial and non-radial models have been presented. This paper proposes a slacks-based non-linear model that guarantees an integer-valued reference point for all integer targets. Also, the reference point of each target is feasible under the proposed model. The lack of a need to round answers to the closest whole value is an advantage of this method. In addition, the results of this model are compared with other models. An example is used to clarify the suggested method. (original abstract)

Słowa kluczowe

PL

Metoda DEA (analiza obwiedni danych); Modele nieliniowe

EN

Data Envelopment Analysis (DEA); Nonlinear models

• Czasopismo: Operations Research and Decisions
• Rocznik: 2022
• Tom: 32
• Numer: nr 3
• Strony: 80-91

Twórcy

autor

Zahra Moazenzadeh

• North Tehran Branch, Islamic Azad University, Tehran, Iran

autor

Saber Saati

• North Tehran Branch, Islamic Azad University, Tehran, Iran

autor

Reza Farzipoor Saen

• College of Economics and Political Science, Sultan Qaboos University, Muscat, Oman

autor

Reza Kazemi Matin

• Islamic Azad University, Karaj, Iran

autor

Sevan Sohraee

• North Tehran Branch, Islamic Azad University, Tehran, Iran

Bibliografia

• [1] Banker, R. D., and Morey, R. C. The use of categorical variables in data envelopment analysis. Management Science 32, 12 (1986), 1613-1627.
• [2] Banker, R. J., Charnes, A., and Cooper, W. W. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 30, 9 (1984), 1078-1092.
• [3] Charnes, A., Cooper, W. W., and Rhodes, E. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 6 (1978), 429-444.
• [4] Chen, C., Ren, J., Tang, L., and Liu, H. Additive integer-valued data envelopment analysis with missing data: A multicriteria evaluation approach. PloS One 15, 6 (2020), 1-20.
• [5] Chen, C.-M., Du, J., Huo, J., and Zhu, J. Undesirable factors in integer-valued DEA: Evaluating the operational efficiencies of city bus systems considering safety records. Decision Support Systems 54, 1 (2012), 330-335.
• [6] de Carvalho Miranda, R., Montevechi, J. A. B., da Silva, A. F., and Marins, F. A. S. Increasing the efficiency in integer simulation optimization: Reducing the search space through data envelopment analysis and orthogonal arrays. European Journal of Operational Research 262, 2 (2017), 673-681.
• [7] Du, J., Chen, C.-M., Chen, Y., Cook, W. D., and Zhu, J. Additive super-efficiency in integer-valued data envelopment analysis. European Journal of Operational Research 218, 1 (2012), 186-192.
• [8] Farrell, M. J. The measurement of productive efficiency. Journal of the Royal Statistical Society: Series A 120, 3 (1957), 253-281.
• [9] Hussain, M. T., Ramli, R., and Khalid, R. A hybrid integer data envelopment analysis based on alternative approach of super slack based measure for measuring super efficiency and inefficiency of decision making units. Far East Journal of Mathematical Sciences (FJMS) 100, 1 (2016), 147-170.
• [10] Jahanshahloo, G. R., and Piri, M. Data envelopment analysis (DEA) with integer and negative inputs and outputs. Journal of Data Envelopment Analysis and Decision Science 2013 (2013), 1-15.
• [11] Jie, T., Yan, Q., and Xu, W. A technical note on "A note on integer-valued radial model in DEA". Computers and Industrial Engineering 87 (2015), 308-310.
• [12] Kamakura, W. A. A note on the use of categorical variables in data envelopment analysis. Management Science 34, 10 (1988), 1273-1276.
• [13] Khezrimotlagh, D., Salleh, S., and Mohsenpour, Z. A new robust mixed integer-valued model in DEA. Applied Mathematical Modelling 37, 24 (2013), 9885-9897.
• [14] Kordrostami, S., Amirteimoori, A., and Noveiri, M. J. S. Inputs and outputs classification in integer-valued data envelopment analysis. Measurement 139 (2019), 317-325.
• [15] Kousmanen, T., and Matin, R. K. Theory of integer-valued data envelopment analysis. European Journal of Operational Research 192, 2 (2009), 658-667.
• [16] Lozano, S., and Villa, G. Data envelopment analysis of integer-valued inputs and outputs. Computers and Operations Research 33, 10 (2006), 3004-3014.
• [17] Rousseau, J. J., and Semple, J. H. Categorical outputs in data envelopment analysis. Management Science 39, 3 (1993), 384-386.
• [18] Taleb, M., Khalid, R., and Ramli, R. 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 (2019), 144-152.
• [19] Tone, K. A slack-based measure of efficiency in data envelopment analysis. European Journal of Operational Research 130, 3 (2001), 498-509.
• [20] Tulkens, H. On FDH efficiency analysis: some methodological issues and applications to retail banking, courts, and urban transit. Journal of Productivity Analysis 4 (1993), 183-210.

Identyfikatory

DOI

10.37190/ord220306