Ranking of Decision-Making Units with Multi-Period Two-Stage Network Structure: a Method Based on Relative Data Envelopment Analysis
Subject Areas : Operation ResearchMaghsoud Ahmad khanlou Gharakhanlou 1 , Nima Azarmir shotorbani 2 , Ghasem Tohidi 3 , Shabnam Razavyan 4 , Rohollah Abbasi 5
1 - PhD Student, Department of Applied Mathematics, Islamic Azad University, Tabriz Branch. Tabriz - Iran
2 - Assistant Professor, Department of Applied Mathematics, Islamic Azad University, Tabriz Branch. Tabriz - Iran
3 - Associate Professor, Department of Mathematics, Islamic Azad University, Tehran Branch. Tehran- Iran.
4 - Associate Professor, Department of Mathematics, Islamic Azad University, South Tehran Branch. Tehran- Iran
5 - Assistant Professor, Department of Mathematics, Qom University. Qom- Iran
Keywords: Multi-period, Efficiency, network, Grading, relative data envelopment analysis,
Abstract :
Data envelopment analysis is always considered as a non-parametric method for measuring the efficiency of a set of decision units. The efficiency number obtained from standard models is a criterion for comparing the performance of each decision unit with other units. Despite the many strengths of these models, one of their weaknesses is the lack of distinction between efficient units. Also, these models do not pay attention to the internal structure of the units and have a black box view. To solve these problems, relational data envelopment analysis models are used, which are much more cost-effective in terms of time and cost; But these models are static and do not take time into evaluation. In this paper, a method has been proposed for grading of the decision making units with multi- period two stages network structure using relative data envelopment analysis. Three different perspective are introduced for assessment of efficiency in time periods via relative data envelopment analysis. Proportionate with each perspective, an efficiency number is obtained for any decision making unit. Then three efficiency numbers obtained in the mentioned method is combined with Shannon entropy method and a total efficiency criterion is defined for each unit. Finally, this measure is considered as the main indicator for the units grading. The results of implementation of the mentioned algorithm on the real example and comparison with the similar methods clarify the strength of this algorithm.
Kamyab, P. Mozaffari, MR. (2021). Cost efficiency in the three-step process of DEA-R network, New Research in Mathematics, Volume 6, Number 23, pp. 147-170.
Adler, N., Volta, N. (2019). Ranking methods within data envelopment analysis. In The Palgrave handbook of economic performance analysis (pp. 189-224). Palgrave Macmillan, Cham.
Aldamak, A., Zolfaghari, S. (2017). Review of efficiency ranking methods in data envelopment analysis. Measurement, 106, 161-172.
Andersen, P., Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management science, 39(10), 1261-1264.
Aparicio, J., Ortiz, L., Pastor, J. T., Zabala-Iturriagagoitia, J. M. (2020). Introducing cross-productivity: a new approach for ranking productive units over time in Data Envelopment Analysis. Computers & industrial engineering.https://doi.org/10.1016/j.cie.2020.106456
Bolouri, M. E., Ziari, S., Ebrahimnejad, A. (2020). New approach for ranking efficient DMUs based on Euclidean norm in data envelopment analysis. International journal of operational research, 37(1), 85-104.
Chen., C., M. (2009). A network-DEA model with new efficiency measures to incorporate the dynamic effect in production networks. European Journal of Operational Research, 194, 687-699.
Despic, O., Paradi, J.C.(2007) : DEA-R: Ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications. Journal of Productivity Analysis. 28,(1 ), pp 33-44.
Fare, R., Grosskopf, S. (2000). Network DEA. Socio-Economic Planning Sciences, 34, 35-49
Holod, D., Lewis, H. F. (2011). Resolving the deposit dilemma: A new DEA bank efficiency model. Journal of Banking and Finance, 35, 2801-2810
Hosseinzadeh Lotfi,F., Ebrahimnejad,A., Vaez-Ghasemi,M., Moghaddas,Z..(2020). Data envelopment analysis with R. Springer International Publishing.
Izadikhah, M., Saen, R. F. (2019). Ranking sustainable suppliers by context-dependent data envelopment analysis. Annals of operations research, 1-31.
Jahangiri, A. (2019). Application of data envelopment analysis technique in Iran banking system. Journal of decisions and operations research, 3(4), 368-401.
Kao, C., Liu, S. T. (2020). A slacks-based measure model for calculating cross efficiency in data envelopment analysis. Omega. https://doi.org/10.1016/j.omega.2020.102192
Liu.WB, Zhang. DQ, Meng. W, Li. XX, Xu. F.(2011). A study of DEA models without explicit inputs. Omega 39, 472-480.
Mozaffar,M.R. , Kamyab,P. , Jablonsky,J. Gerami,J.(2014). Cost and revenue efficiency in DEA-R models, Computers & Industrial Engineering.78 ,188–194.
Mozaffari. M.R, Dadkhah.F, Jablonsky.J, Fernandes Wanke.P.(2020). Finding efficient surfaces in DEA-R models, Applied Mathematics and Computation, 386,125497, 1-14
Mozaffaria, M.R. , Saneib ,M., Jablonsky,J. (2017). Efficiency Analysis in Multi-Stage Network DEA-R Models, Int. J. Data Envelopment Analysis , Vol.5, No.2: 1553-1572.
Moghaddas,Z., Vaez-Ghesemi,M. , Hosseinzadeh Lotfi,F., FarzipoorSaen,R. (2020). Stepwise pricing in evaluating revenue efficiency in Data Envelopment Analysis: A case study in power plants. scientia iranica. DOI.10.24200/SCI.55350.4184.
Moghaddas, Z., Tosarkani, B.M., Yousefi, S.(2022). A Developed Data Envelopment Analysis Model for Efficient Sustainable Supply Chain Network Design. Sustainability, 14, 262.
Moghaddas,Z. Amirteimoori,A., Kazemi Matin,R.(2022). Selective proportionality and integer-valued data in DEA: an application to performance evaluation of high schools. Operational Research. Springer Berlin. Heidelberg, 1-25
Nemoto, J., Goto, M. (1999). Dynamic data envelopment analysis: Modeling intertemporal behavior of a firm in the presence of productive inefficiencies. Economics Letters, 64, 51-56.
Nemoto, J., Goto, M. (2003). Measurement of dynamic efficiency in production: An application of data envelopment analysis to Japanese electric utilities. Journal of Productivity Analysis, 19, 191-210.
Ostovan,S, Mozaffari,M.R., Jamshidi,A.(2020), Gerami,J., Evaluation of Two-Stage Networks Based on Average Efficiency Using DEA and DEA-R with Fuzzy Data, Int. J. Fuzzy Syst.
Shanian, A., Savadogo, O. (2006). A material selection model based on the concept of multiple attribute decision making Materials and Design, 27, 329–337
Si, Q., Ma, Z. (2019). DEA cross-efficiency ranking method based on grey correlation degree and relative entropy. Entropy, 21(10), 966.
Soleimani-Chamkhorami, K., Hosseinzadeh Lotfi, F., Jahanshahloo, G., & Rostamy-Malkhalifeh, M. (2020). A ranking system based on inverse data envelopment analysis. IMA journal of management mathematics, 31(3), 367-385.
Soleimani-Damaneh, M., Zarepisheh, M. (2009). Shannon’s entropy for combining the efficiency results of different DEA models: Method and application. Expert systems with applications, 36(3), 5146-5150.
Tohidnia, S., Tohidi, G. (2019). Estimating multi-period global cost efficiency and productivity change of systems with network structures. Journal of Industrial Engineering International, 15, 171-179.
Wang, T.C. and Lee, H.D. (2009). Developing a fuzzy TOPSIS approach based on subjective weights and objective weights, Expert Systems with Applications, 36, 8980– 8985.
Wei. C.K , Chen.L.C., Li. R.K, Tsai.C.H. (2011a). Using the DEA-R model in the hospital industry to study the pseudo-inefficiency problem, Expert Systems with Applications, 38 (3)2172–2176
Wei. C.K, Chen. L.C., Li. R.K, Tsai.C.H. (2011c). Exploration of efficiency underestimation of CCR model: Based on medical sectors with DEA-R model, Expert Systems with Applications, 38 (3) 3155–3160.
Wei. C.K, Chen.L.C., Li. R.K, Tsai.C.H. (2011b). A study of developing an input-oriented ratio-based comparative efficiency model, Expert Systems with Applica- tions, 38 (2) 2473–2477.
Wu, J.Z. and Zhang, Q. (2011). Multi criteria decision making method based on intuitionistic fuzzy weighted entropy, Expert Systems with Applications, 38, pp. 916–922
Zhang, H., Gu, C.L., Gu, L.W. and Zhang, Y. (2010)."The evaluation of tourism destination competitiveness by TOPSIS & information entropy – A case in the Yangtze River Delta of China", Tourism Management, 32, 2, 443-451.
Zhao, X., Qi, Q. Li, R. (2010)."The establishment and application of fuzzy comprehensive model with weight based on entropy technology for air quality assessment", Symposium on Security Detection and Information Processing, 7, 217–222.