Evaluation of Decision-Making Units with Interval Grey Data in DEA
محورهای موضوعی : فصلنامه ریاضی
Jafar Pourmahmoud
1
,
Mahdi Eini
2
,
Davood Darvishi Salokolaei
3
,
Saeid Mehrabian
4
1 - Department of Applied Mathematics, Azarbaijan Shahaid Madani University,Tabriz, Iran.
2 - Department of Applied Mathematics, Azarbaijan Shahaid Madani University,Tabriz, Iran.
3 - Department of Mathematics, Payame Noor University, Tehran, Iran
4 - Department of Computer Science, Faculty of Mathematics Sciences and Computer, Kharazmi University, Karaj, Iran
کلید واژه: Efficiency, Stroke, Interval grey number, Data Envelopment Analysis.,
چکیده مقاله :
When evaluating the efficiency of decision-making units, paying attention to the amount of indicators and their conditions is of particular importance. In classical data envelopment analysis models, inputs and outputs are deterministic. However, if the data is grey, to obtain reliable results, it is better to use the theory of grey systems in data envelopment analysis. In this paper, a new method for using interval grey data in CCR model is proposed. The proposed method on a practical example is used to check the condition of cerebral hemorrhage in stroke patients after the injection of Tissue Plasminogen Activator. The results obtained from the proposed method on this example show that the examination of cerebral hemorrhage status of stroke patients is more accurately calculated and these results are more reliable for decision makers.
When evaluating the efficiency of decision-making units, paying attention to the amount of indicators and their conditions is of particular importance. In classical data envelopment analysis models, inputs and outputs are deterministic. However, if the data is grey, to obtain reliable results, it is better to use the theory of grey systems in data envelopment analysis. In this paper, a new method for using interval grey data in CCR model is proposed. The proposed method on a practical example is used to check the condition of cerebral hemorrhage in stroke patients after the injection of Tissue Plasminogen Activator. The results obtained from the proposed method on this example show that the examination of cerebral hemorrhage status of stroke patients is more accurately calculated and these results are more reliable for decision makers.
[1]A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research 2 (1978) 429-444. [2]C. N. Wang, K. N. C. Imperial, C. C. Huang, T. T. Dang, Output targeting and runway utilization of major international airports: A comparative analysis using DEA, Mathematics, 10.4 (2022) 551. [3]H. M. A. Ilyas, M. Safa, A. Bailey, S. Rauf, A. Khan, Energy efficiency outlook of New Zealand dairy farming systems: An application of data envelopment analysis (DEA) approach, Energies, 13.1 (2020) 251. [4]S. Ang, R., Zheng, F. Wei, F. Yang, A modified DEA-based approach for selecting preferred benchmarks in social networks, Journal of the Operational Research Society, 72.2 (2021) 342-353. [5]T. R. Nunamaker, Measuring routine nursing service efficiency: a comparison of cost per patient day and data envelopment analysis models, Health services research 18.2 Pt 1 (1983) 183. [6]I. K. Kleinsorge, D. F. Karney. Management of nursing homes using data envelopment analysis, Socio-Economic Planning Sciences 26.1 (1992) 57-71. [7]K. Ersoy, S. Kavuncubasi, Y. A. Ozcan, II, J. M Harris, Technical efficiencies of Turkish hospitals: DEA approach, Journal of Medical Systems 21 (1997) 67-74. [8]A. I. Zavras, G. Tsakos, C. Economou, J. Kyriopoulos, Using DEA to evaluate efficiency and formulate policy within a Greek national primary health care network, Journal of Medical Systems 26 (2002) 285-292. [9]M. D. Basson, T. Butler, Evaluation of operating room suite efficiency in the Veterans Health Administration system by using data-envelopment analysis, The American journal of surgery, 192.5 (2006) 649-656. [10]P. Marschall, S. Flessa, Efficiency of primary care in rural Burkina Faso. A two-stage DEA analysis, Health economics review, 1 (2011) 1-15. [11]C., Popescu, L., Asandului, P. Fatulescu, A data envelopment analysis for evaluating Romania's health system, Procedia-Social and Behavioral Sciences, 109 (2014) 1185-1189. [12]S., Kohl, J., Schoenfelder, A. Fügener, J. O. Brunner, The use of Data Envelopment Analysis (DEA) in healthcare with a focus on hospitals, Health care management science, 22 (2019) 245-286. [13]B. Gavurova, K. Kocisova, J. Sopko, Health system efficiency in OECD countries: dynamic network DEA approach, Health Economics Review, 11 (2021) 1-25. [14]A. S. Omir, A. Z. Panzabekova, A. A, Satybaldin, Evaluating the Financial Efficiency of the Healthcare System: A Three-Stage DEA Model Analysis. R-Economy. 49.4 (2023) 353-365. [15]M. Zadmirzaei, F. Hasanzadeh, A. Susaeta, E. Gutiérrez , A novel integrated fuzzy DEA–artificial intelligence approach for assessing environmental efficiency and predicting CO2 emissions. Soft Computing, 28.1 (2024) 565-591. [16]H. Pourbabagol, M. Amiri, M. T. Taghavifard, P. Hanafizadeh, A new fuzzy DEA network based on possibility and necessity measures for agile supply chain performance evaluation: A case study, Expert Systems with Applications, 220 (2023) 119552. [17]M.Bagheri, A., Ebrahimnejad, S. Razavyan, F. Hosseinzadeh Lotfi, , N. Malekmohammadi, Fuzzy arithmetic DEA approach for fuzzy multi-objective transportation problem, Operational Research, (2022): 1-31. [18]A. Hadi-Vencheh, M. Khodadadipour, Y.Tan, H. Arman, D. Roubaud, Cross-efficiency analysis of energy sector using stochastic DEA: Considering pollutant emissions, Journal of Environmental Management, 364 (2024) 121319. [19]H. Omrani, M. Shamsi, A. Emrouznejad, T. Teplova, A robust DEA model under discrete scenarios for assessing bank branches, Expert Systems with Applications, 219 (2023) 119694. [20]A., Amirteimoori, B. K. Sahoo, V. Charles, S. Mehdizadeh, A. Amirteimoori, B. K. Sahoo, V. Charles, S. Mehdizadeh, Stochastic Data Envelopment Analysis, Stochastic Benchmarking: Theory and Applications, (2022) 55-76. [21]E. Vaezi, S. E. Najafi, S. M. Haji Molana, F. Hosseinzadeh Lotfi, M. Ahadzadeh Namin, Measuring performance of a hybrid system based on imprecise data: Modeling and solution approaches. Journal of Industrial Engineering and Management Studies, 6.2 (2019) 214-241. [22]M., Toloo, E. Keshavarz, A. Hatami-Marbini, An interval efficiency analysis with dual-role factors, Or Spectrum, 43 (2021) 255-287. [23]B. Jiang, C. Yang, Q. Dong, J. Li, Ecological efficiency evaluation of China’s port industries with imprecise data, Evolutionary Intelligence, (2024) 1-12. [24]R. K. Shiraz, H., Fukuyama, J. Vakili, , A note on, some new ranking criteria in data envelopment analysis under uncertain environment, Computers & Industrial Engineering, 131 (2019) 259-262. [25]J. Pourmahmoud, N. Bagheri, Providing an uncertain model for evaluating the performance of a basic two-stage system, Soft Computing, 25 (2021) 4739-4748. [26]B. Jiang, E. Chi, J. Li, Uncertain Data Envelopment Analysis for Cross Efficiency Evaluation with Imprecise Data, Mathematics, 10.13 (2022) 2161. [27]J.L. Deng, The control problems of grey systems”, Systems and Control Letters, 1 5 (1982) 288-294. [28]U.R,Tuzkaya E. Yolver , R&D Project selection by integrated gray analytic network process and gray relational analysis: An implementation for home appliances company, Aeronau Space Technol. 8.2 (2015) 35-41. [29]M.H. Kamfiroozi, A. Aliahmadi, M. Jafari Eskandari, Application Application of Three Parameter Interval Grey Numbers in Enterprise Resource Planning Selection, Int J Inform Secur Sys Manag. (2012) 72-77. [30]H.Yan, L. Zhang, The research of the grey system theory applied on buildings deformation monitoring”, Journal of Chemical and Pharmaceutical Research, 6.7 (2014) 2627-2629. [31]A. Mahmoudi, S.A. Javed, Grey multiple criteria decision making methods: a literature review, ICSES Transaction on Neural and Fuzzy Computing, 2.2 (2019) 1-13. [32]M. Zhang, H. Guo, M. Sun, S. Liu, J. Forrest, A novel flexible grey multivariable model and its application in forecasting energy consumption in China, Energy, 239 (2022) 122441. [33]D. Tiwari, A. F. Sherwani, M. Asjad, A. Arora, Grey relational analysis coupled with principal component analysis for optimization of the cyclic parameters of a solar-driven organic Rankine cycle, Grey Systems: Theory and Application, 7.2 (2017) 218-235. [34]S. Liu, Y. Lin, Grey information: theory and practical applications, Springer Science & Business Media, (2006). [35]S. D. Guo, S. Liu, Z. Fang, Algorithm rules of interval grey numbers based on different “kernel” and the degree of greyness of grey numbers, Grey Systems: Theory and Application, 7.2 (2017) 168-178. [36]P. Li, C. Wei, A new two-stage grey evaluation decision-making method for interval grey numbers, Kybernetes, 47.4 (2018) 801-815. [37]K. Chen, P. Chen, L. Yang, L. Jin, Grey clustering evaluation based on AHP and interval grey number, International Journal of Intelligent Computing and Cybernetics, 12.1 (2019) 127-137. [38]X. Li, L. Li, One ranking method of interval grey number based on generalised greyness, Grey Systems: Theory and Application, 13.2 (2023) 340-356. [39]X. Li, X. Liao, X. Tan, H. Wang, Using grey relational analysis to evaluate resource configuration and service ability for hospital on public private partnership model in China, Grey Systems: Theory and Application, 4.2 (2014) 260-272. [40]C. Delcea, B. Ioana-Alexandra, Fostering risk management in healthcare units using grey systems theory, Grey Systems: Theory and Application, 6.2 (2016) 216-232. [41]K. Pourmohammadi, P. Shojaei, H. Rahimi, P. Bastani, Evaluating the health system financing of the Eastern Mediterranean Region (EMR) countries using Grey Relation Analysis and Shannon Entropy, Cost Effectiveness and Resource Allocation, 16 (2018) 1-9. [42]S.A. Javed, S. Liu, A. Mahmoudi, M. Nawaz, Patients’ satisfaction and public and private sectors’ health care service quality in Pakistan: application of grey decision analysis approaches, the International Journal of Health Planning and Management, 34.1 (2019) 168-182. [43]X. Peng, X. Tang, Y. Chen, J. Zhang, Ranking the healthcare resource factors for public satisfaction with health system in China—based on the grey relational analysis models, International Journal of Environmental Research and Public Health, 18.3 (2021) 995. [44]E. Çetin, H. Özen, Ranking eHealth Efforts of Countries to Fight Coronavirus Pandemic via Grey Systems Theory: Evidence from National COVID-19 Mobile Apps. In Integrity, Transparency and Corruption in Healthcare & Research on Health, Singapore: Springer Nature Singapore, 2 (2023) 143-178. [45] Y.S. Yang, Data envelopment analysis (DEA) model with interval gray numbers, International journal of information and management sciences, 9.4 (1998)11-23. [46]R. T.Wang, C. T. B. Ho, K. Oh, Measuring production and marketing efficiency using grey relation analysis and data envelopment analysis, International Journal of Production Research, 48.1 (2010) 183-199. [47]J. Wang, S. Liu, Efficiency measures in DEA with grey interval data under the hypotheses of data consistency, Grey Systems: Theory and Application, 2.1 (2012) 63-69. [48]L. W. Wang, T. T. Tran, N. T. Nguyen, An empirical study of hybrid DEA and grey system theory on analyzing performance: a case from Indian mining industry, Journal of Applied Mathematics, 2015.1 (2015) 395360. [49]C. N. Wang, T. T. Tsai, H. P. Hsu, L. H. Nguyen, Performance evaluation of major Asian airline companies using DEA window model and grey theory. Sustainability, 11 9 (2019) 2701. [50]C. N. Wang, T. T. Dang, N. A. T. Nguyen, T. T. H. Le, Supporting better decision-making: A combined grey model and data envelopment analysis for efficiency evaluation in e-commerce marketplaces. Sustainability, 12 24 (2020) 10385. [51]T. T. Tran, N. T. Nguyen, Applying Data Envelopment Analysis and Grey Model for the Productivity Evaluation of Vietnamese Tourism. Industrial Engineering & Management Systems, 22 3 (2023) 298-312. [52] J. Pourmahmoud, M. Eini, D. Darvishi Salokolaei, S. Mehrabian, Hybrid model for evaluation of DMUs with principles of strong and weak disposability in the presence of grey undesirable factors, Iranian Journal Of Operations Research, 140.2, 32-46. [53]S.H. Nasseri, A. Yazdani, D. Darvishi salikolaei, ,A primal simplex algorithm for solving linear programming problem with grey cost coefficients, Journal of New Researches in Mathematics, 1.4 (2016) 115-135. [54]B.Q. Hu, S. Wang, A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers, Journal of Industrial and Management Optimization, 2.4 (2006) 351-371. [55]J.H. Wu, C.B. Chen, An alternative form for grey relational grades, the journal of Grey System, 11 1 (1999) 7-12. [56] A. Charnes, W. W.Cooper, Programming with linear fractional functionals, Naval Research logistics quarterly, 9.3-4 (1962)181-186. [57] M. S. Bazaraa, H. D. Sherali, C. M. Shetty, Nonlinear programming: theory and algorithms, John wiley & sons, (2013). [58] S. Mehrabian, G. R. Jahanshahloo, M. R. Alirezaee, G. R. Amin, , An assurance interval for the non-Archimedean epsilon in DEA models, Operations Research, 48.2 (2000) 344-347. [59] L.B. Goldstein, D.B. Matchar, Clinical assessment of stroke, Amer. Med. Assoc, 271 (1994) 1114–1120.
