The sustainability radius of the cost efficiency in Interval Data Envelopment Analysis: A case study from Tehran Stocks

الموضوعات :

Esmaeil Mombini ¹ , Mohsen Rostamy-Malkhalifeh ² , Mansour Saraj ³

1 - Department of mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
2 - Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran|Department of mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

تاريخ الإرسال : 24 الأربعاء , ربيع الثاني, 1442 تاريخ التأكيد : 17 الأحد , ذو القعدة, 1442 تاريخ الإصدار : 29 الجمعة , شعبان, 1443

الکلمات المفتاحية: Cost efficiency, Sensitivity analysis, Interval data, Data envelopment analysis, Sustainability radius,

ملخص المقالة :

Interval Data Envelopment Analysis (Interval DEA) is a methodology to assess the efficiency of decision-making units (DMUs) in the presence of interval data. Sensitivity analysis and sustainability evaluation of decision- making units are as the most important concerns of Decision Makers (DM). In the past decades, many scholars have been attracted to the sustainability evaluation of DMUs from different perspectives. This study focuses on the sensitivity analysis in DEA and proposes an approach to determine the sustainability radius of the cost efficiency of units with interval data. Potential application of our proposed methods is illustrated by a numerical example from the literature review.

المصادر:

References

[1] Allahyar, M., Rostamy-Malkhalifeh, M., Negative data in data envelopment analysis: Efficiency analysis and estimating returns to scale, Computers and Industrial Engineering, 2015, 82, P.78-81.

 Doi: 10.1016/j.cie.2015.01.022

[2] Amirteimoori, A., and Kordrostami, S., Azizi, H., Measurement of overall performances of decision making units in the presence of interval data, International Journal of operational Research, 2017, 28(4), P.429-447.

 Doi: 10.1504/IJOR.2017.082607

[3] Anderson, P., Peterson, N.C. A procedure for ranking efficient units in Data Envelopment Analysis, Management Science, 1993, 39, P.1261-1264. Doi: 10.1287/mnsc.39.10.1261

[4] Azizi, H., Amirteimoori, A. and Kordrostami, S., A note on dual models of interval DEA and its extension to interval data, International Journal of Industrial Mathematics, 2017, 10(2), P.115-130.

[5] Banker, R.D., Charnes, A., Cooper, W.W., Some models for estimating technical and scale inefficiencies in DEA, Management Science, 1984, 30, P.1078-1092. Doi: 10.1287/mnsc.30.9.1078

[6] Camanho, A. S., Dyson, R. G., Cost efficiency measurement with price uncertainty: a DEA application to bank branch assessments, European journal of operational research, 2005, 161(2), P.432-446.

 Doi: 10.1016/j.ejor.2003.07.018

[7] Charnes, A., Cooper, W.W., Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 1978, 2, P. 429-444. Doi: 10.1016/0377-2217(78)90138-8

[8] Charnes, A., Cooper, W. W., Lewin, A. Y., Morey, R. C., Rousseau, J., Sensitivity and stability analysis in DEA, Annals of Operations Research, 1984, 2(1), P.139-156. Doi: 10.1007/BF01874736

[9] Charnes, A., Rousseau, J. J., Semple, J. H., Sensitivity and stability of efficiency classifications in data envelopment analysis, Journal of productivity analysis, 1996, 7(1), P.5-18. Doi: 10.1007/BF00158473

[10] Cherchye, L., De Rock, B., Vermeulen, F., Analyzing cost-efficient production behavior under economies of scope: A nonparametric methodology, Operations Research, 2008, 56(1), P.204-221.

Doi: 10.1287/opre.1070.0388

[11] Cinaroglu, S., Oncology services efficiency in the age of pandemic: A jackknife and bootstrap sensitivity analysis for robustness check of DEA scores, Journal of Cancer Policy, 2021, 27, P.100-262.

Doi: 10.1016/j.jcpo.2020.100262

[12] Cooper, W.W., Park, K.S., Yu, G., IDEA and AR-IDEA: models for dealing with imprecise data in DEA, Management Science, 1999, 45, P.597-607. Doi: 10.1287/mnsc.45.4.597

[13] Cooper, W. W., Thompson, R. G., Thrall, R. M., Introduction: Extensions and new developments in DEA, Annals of operations Research, 1996, 66(1), P.1-45. Doi: 10.1007/BF02125451

[14] Cooper, W.W., Park, K.S., Yu, G., IDEA (imprecise data envelopment analysis) with CMDs (column maximum decision- making units, Journal of the Operational Research Society, 2001, 52(2), P.176-181.

Doi: 10.1057/palgrave.jors.2601070

[15] Despotis, D.K., and Smirlis, Y.G., Data envelopment analysis with imprecise data, European Journal of Operational Research, 2002, 140, P.24-36. Doi: 10.1016/S0377-2217(01)00200-4

[16] Ebrahimi, B., Efficiency distribution and expected efficiencies in DEA with imprecise data, Journal of Industrial and Systems Engineering, 2019, 12(1), P.185-197.

[17] Entani, T., Maeda, Y., and Tanaka, H., Dual models of interval DEA and its extension to interval data, European Journal of Operational Research, 2002, 136, P.32-45. Doi: 10.1016/S0377-2217(01)00055-8

[18] Yang, G.L., and Emrouznejad, A., Modelling efficient and anti-efficient frontiers in DEA without explicit inputs, International Journal of Operational Research, 2019, 35(4), P.505-528. Doi: 10.1504/IJOR.2019.10022812

[19] Esmaeili, M., An Enhanced Russell Measure in DEA with interval data, Applied Mathematics and Computation, 2012, 219, P.1589-1593. Doi: 10.1016/j.amc.2012.07.060

[20] Fang, L., Li, H.,   A comment on “cost efficiency in data envelopment analysis with data uncertainty, European journal of operational research, 2012, 220(2), P.588-590. Doi: 10.1016/j.ejor.2012.01.053

[21] Färe, R., Grosskopf, S., A nonparametric cost approach to scale efficiency, The Scandinavian Journal of Economics, 1985, P.594-604. Doi: 10.2307/3439974

[22] Färe, R., Grosskopf, S., and Lovell, C.A.K., The measurement of efficiency of production, Kluwer-Nijhoff, Boston, 1985.

[23] Farrel, M. J., The Measurement of Productive Efficiency. MJ Farrell, Journal of the Royal Statistical Society, SeriesA (General), 1957, 120(3), P. 253-290. Doi: 10.2307/2343100

[24] Ghyasi, A., An investigation of the relationship between earnings management and financial ratios (Panel data approach), International Journal of Economics and Financial Issues, 2017, 7(1). P. 608-612.

[25] Hatami-Marbini, A., Emrouznejad, A. and Agrell, P.J. Interval data without sign restrictions in DEA, Applied Mathematical Modelling, 2014, 38, P.2028-2036. Doi: 10.1016/j.apm.2013.10.027

[26] He, F., Xu, X., Chen, R., Zhang, N., Sensitivity and stability analysis in DEA with bounded uncertainty, Optimization Letters, 2016, 10(4), P.737-752. Doi: 10.1007/s11590-015-0895-2

[27] Jabbari, A., Hosseinzadehlotfi, F., Jahanshahloo, G., Rostamy-Malkhalifeh, M., Ranking all units with non-radial models in DEA. International Journal of Nonlinear Analysis and Applications, 2019, 10(2), P. 111-129. Doi: 10.22075/ijnaa.2019.4179

[28] Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., and Moradi, M., Sensitivity and stability analysis in DEA with interval data, Applied Mathematics and Computation, 2004, 156, P.463-477. Doi: 10.1016/j.amc.2003.08.005

[29] Jahanshahloo, G. R., Soleimani-Damaneh, M., Mostafaee, A., Cost efficiency analysis with ordinal data: A theoretical and computational view, International Journal of Computer Mathematics, 2007, 84(4), P.553-562. Doi: 10.1080/00207160701242243

[30] Jiang, B., Lio, W., Li, X., An Uncertain DEA Model for Scale Efficiency Evaluation, IEEE Transaction on Fuzzy Systems, 2018, P.1-9. Doi: 10.1109/TFUZZ.2018.2883546.

[31] Kao, C., and Liu, S., Scale Efficiency Measurement in Data Envelopment Analysis with Interval Data: A Two-Level Programming Approach, Journal of CENTRUM Cathedra, 2011, 4, P.224-235. Doi: 10.7835/jcc-berj-2011-0060

[32] Kim, S.H., Park, C.K., and Park, K.S., An application of data envelopment analysis in telephone offices evaluation with partial data, Computers and Operations Research, 1999, 26, P.59-72. Doi: 10.1016/S0305-0548(98)00041-0

[33] Kordrostami, S., Jahani Sayyad Noveiri, M., Evaluating the performance and classifying the interval data in data envelopment analysis, International Journal of Management Science and Engineering Management, 2014, 9(4), 243-248. Doi: 10.1080/17509653.2014.900655

[34] Kuosmanen, T., Post, T., Measuring economic efficiency with incomplete price information, European Journal of Operational Research, 2003, 144(2), P.454-457. Doi:10.1016/S0377-2217(00)00237-X

[35] Kuosmanen, T., Post, T., Measuring economic efficiency with incomplete price information: With an application to European commercial banks, European journal of operational research, 2001, 134(1), P.43-58.

Doi:10.1016/S0377-2217(00)00237-X

[36] Lee, Y.K., Park, K.S., Identification of inefficiencies in an additive model based IDEA, Computers and Operations Research, 2002, 29, P.1661-1676. Doi: 10.1016/S0305-0548(01)00049-1

[37] Maniadakis, N., Thanassoulis, E., A cost Malmquist productivity index, European Journal of Operational Research, 2004, 154(2), P.396-409. Doi: 10.1016/S0377-2217(03)00177-2

[38] Mirdehghan, S. M., Vakili, J., Relations Among Technical, Cost and Revenue Efficiencies in Data Envelopment Analysis, International Journal of Applied Mathematics, 2015, 45(4), P. 1-10.

[39] 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

[40] Izadikhah, M., Azadi, M., Toloo, M., Hussain, F.K., Sustainably resilient supply chains evaluation in public transport: A fuzzy chance-constrained two-stage DEA approach, Applied Soft Computing, 2021, 113(B), Doi: 10.1016/j.asoc.2021.107879.

[41] 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

[42] 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

[43] Izadikhah, M., A Fuzzy Goal Programming Based Procedure for Machine Tool Selection, 2015, 28(1), P. 361-372, Doi: 10.3233/IFS-141311

[44] 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

[45] Mostafaee, A., Saljooghi, F. H., Cost efficiency measures in data envelopment analysis with data uncertainty. European journal of operational research, 2010, 202(2), P.595-603. Doi: 10.1016/j.ejor.2009.06.007

[46] Park, K.S., Efficiency bounds and efficiency classifications in DEA with imprecise data, Journal of the Operational Research Society, 2007, 58, P.533-540. Doi: 10.1057/palgrave.jors.2602178

[47] Park, K.S. Duality, efficiency computations and interpretations in imprecise DEA, European Journal of Operational Research, 2010, 200, P.289-296. Doi: 10.1016/j.ejor.2008.11.028

[43] Sahoo, B. K., Kerstens, K., & Tone, K. Returns to growth in a nonparametric DEA approach. International Transactions in Operational Research, 2012, 19(3), P.463-486. Doi: 10.1111/j.1475-3995.2012.00841.x

[45] Seiford, L. M., & Zhu, J. Sensitivity analysis of DEA models for simultaneous changes in all the data. Journal of the Operational Research Society, 1998, 49(10), P.1060-1071. Doi: 10.1057/palgrave.jors.2600620

[44] Sengupta, J. K., & Sahoo, B. Efficiency models in data envelopment analysis: Techniques of evaluation of productivity of firms in a growing economy. Springer, 2006.

[45] Seyed Esmaeili, F. S., Rostamy-Malkhalifeh, M., & Hosseinzadeh Lotfi, F. Two-Stage Network DEA Model Under Interval Data. Mathematical Analysis and Convex Optimization, 2020, 1(2), P.101-106. Doi: 10.29252/maco.1.2.10

[46] Sharma, M., & Mehra, A. Departmental Efficiency of Panjab University: An Analysis Using Dea and Tobit Model. Economic Affairs, 2019, 64(4), P.769-781. Doi: 10.30954/0424-2513.4.2019.12

[47] Smirlis, Y.G., Maragos, E.K. and Despotis, D.K. Data envelopment analysis with missing values: an interval DEA approach, Applied Mathematics and Computation, 2006, 177(1), P. 1-10. Doi: 10.1016/j.amc.2005.10.028

[48] Soleimani-Chamkhorami, K., Hosseinzadeh Lotfi, F., Jahanshahloo, G., & Rostamy-Malkhalifeh, M. A ranking system based on inverse data envelopment analysis. IMA Journal of Management Mathematics, 2020, 31(3), P.367-385. Doi: 10.1093/imaman/dpz014

[49] Sueyoshi, T. Measuring efficiencies and returns to scale of Nippon Telegraph & Telephone in production and cost analyses. Management Science, 1997, 43(6), P.779-796. Doi: 10.1287/mnsc.43.6.779

[50] Sun, J., Miao, Y., Wu, J., Cui, L. and Zhong, R. Improved interval DEA models with common weight, Kybernetika, 2014, 50(5), P.774-785. Doi: 10.14736/kyb-2014-5-0774

[51] Tohidnia, S., Tohidi, G., Estimating multi-period global cost efficiency and productivity change of systems with network structures, Journal of Industrial Engineering International, 2019, 15(1), P.171-179. Doi: 10.1007/s40092-018-0254-x

[52] Toloo, M., Aghayi, N., and Rostamy-malkhalifeh, M., Measuring overall profit efficiency with interval data, Applied Mathematics and Computation, 2008, 201, P.640–649. Doi: 10.1016/j.amc.2007.12.061

[53] Toloo, M., Keshavarz, E., Hatami-Marbini, A., Dual-role factors for imprecise data envelopment analysis Omega, 2018, 77, P.15-31. Doi: 10.1016/j.omega.2017.05.005

[54] Tone, K. A strange case of the cost and allocative efficiencies in DEA, Journal of the Operational Research Society, 2002, 53(11), P.1225-1231. Doi: 10.1057/palgrave.jors.2601438

[55] Tone, K., Sahoo, B. K., Evaluating cost efficiency and returns to scale in the Life Insurance Corporation of India using data envelopment analysis, Socio-Economic Planning Sciences, 2005, 39(4), P.261-285.

 Doi: 10.1016/j.seps.2004.06.001

[56] Tone, K., Sahoo, B. K., Re-examining scale elasticity in DEA, Annals of Operations Research, 2006, 145(1), P.69-87. Doi: 10.1007/s10479-006-0027-6

[57] Wang, Y.M., Greatbanks, R. and Yang, J.B., Interval efficiency assessment using data envelopment analysis, Fuzzy Sets and Systems, 2015, 153, P.347-370. Doi: 10.1016/j.fss.2004.12.011

[58] Yang, L. H., Liu, J., Wang, Y. M., Martínez, L., New activation weight calculation and parameter optimization for extended belief rule-based system based on sensitivity analysis, Knowledge and Information Systems, 2019, 60(2), P.837-878. Doi: 10.1007/s10115-018-1211-0

[59] Zhu, J., Imprecise data envelopment analysis (IDEA): a review and improvement with an application, European Journal of Operational Research, 2003, 144, P.513-529. Doi: 10.1016/S0377-2217(01)00392-7