Data envelopment analysis with imprecise data revisited

Subject Areas : Applied Mathematics Modeling

Mohammad Izadikhah ¹ , Dimitris K. Despotis ²

1 - Department of Mathematics, College of Science, Arak Branch, Islamic Azad University, P.O. Box: 38135/567, Arak, Iran
2 - Department of Informatics, University of Piraeus, Greece

Received: 2022-02-12 Accepted : 2022-01-17 Published : 2022-05-01

Keywords: interval efficiency, Data envelopment analysis, Interval data,

Abstract :

Wang et al. (2005) proposed a pair of data envelopment analysis (DEA) models to deal with the efficiency assessment of decision-making units (DMU) in the presence of interval input/output data. Their approach was developed with reference to an earlier approach proposed by Despotis and Smirlis (2002) for the same problem. Given that the input/output data are given as interval numbers, the efficiency scores are interval measures as well. In such a setting, both approaches provide lower and upper bounds for the efficiency scores. Wang et al. (2005) claim that the lower and upper bounds calculated in Despotis and Smirlis (2002) are incorrect. Then, they present different models to calculate the true bounds. In this paper, we counter-argue their claim and we show that the Despotis and Smirlis bounds are correct and those provided in Wang et al. are estimated in a manner that they fail to satisfy an obvious property that they should possess. We illustrate our arguments with a counterexample that was originally used in Wang et. al (2005).

References:

[1] Charnes, A., Cooper, W. W., Rhodes, E., Measuring the efficiency of decision making units. European Journal of Operational Research, 1978; 2(6): 429-444.

[2] Cooper, W.W.  Park, K.S. & Yu, G. IDEA and AR-IDEA: Models for dealing with imprecise data in DEA, Management Science, 1999; 45: 597–607.

[3] Despotis, D. K., & Smirlis, Y. G., Data envelopment analysis with imprecise data. European Journal of Operational Research, 2002; 140(1): 24-36.

[4] Wang, Y.-M., Greatbanks, R., & Yang, J.-B., Interval efficiency assessment using data envelopment analysis. Fuzzy Sets and Systems, 2005; 153(3): 347-370.

[5] Izadikhah, M., Farzipoor Saen, R. Solving voting system by data envelopment analysis for assessing sustainability of suppliers. Group Decis Negot, 2019, 28, P. 641–669. Doi: 10.1007/s10726-019-09616-7

[6] Poordavoodi, A., Reza, M., Haj, H., Rahmani, A. M., Izadikhah, M., Toward a More Accurate Web Service Selection Using Modified Interval DEA Models with Undesirable Outputs. CMES-Computer Modeling in Engineering & Sciences, 2020, 123(2), P. 525–570. Doi: 10.32604/cmes.2020.08854

[7] Azadi, M., Izadikhah, M., Ramezani, F., Hussain, F.K., A mixed ideal and anti-ideal DEA model: an application to evaluate cloud service providers, IMA Journal of Management Mathematics, 2000, 31(20), P. 233–256, Doi: 10.1093/imaman/dpz012

[8] Izadikhah, M. Financial Assessment of Banks and Financial Institutes in Stock Exchange by Means of an Enhanced Two stage DEA Model. Advances in Mathematical Finance and Applications, 2021, 6(2), P. 207-232. Doi: 10.22034/amfa.2020.1910507.1491