Inverse Data Envelopment Analysis to Estimate Inputs with Triangular Fuzzy Numbers
الموضوعات : International Journal of Data Envelopment AnalysisMohammad Taghi Yahyapour-Shikhzahedi 1 , sohrab kordrostami 2 , S Edalatpanah 3 , Alireza Amirteimoori 4
1 - گروه ریاضی، واحد لاهیجان،دانشگاه آزاد اسلامی، لاهیجان، ایران.
2 - Department of mathematics, Islamic azad University of Lahijan, Lahjan, Iran
3 - Islamic Azad University, Iran
4 - Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
الکلمات المفتاحية: Inverse data envelopment analysis, improving cost efficiency, increasing outputs, membership function, triangular fuzzy numbers,
ملخص المقالة :
In the real world, all available data are not definitive and are considered based on quality. Estimating the values of the inputs when we change the values of the outputs as desired is one of the important applications of inverse data envelopment analysis. If we want to estimate the level of inputs (outputs) among a group of decision-making units (DMUs), when some or all of its outputs (inputs) are changed so that cost efficiency is maintained or improved, inverse data envelopment analysis is used. In this article, cost efficiency is investigated by increasing desired outputs along with triangular fuzzy data. The problem of inverse data envelopment analysis with fuzzy data is presented for the cost efficiency of the DMU under evaluation. Also, in this connection, the results of the proposed model will be examined in a numerical example.
1. Ebrahimnejad, A., Nasseri, S.H., Lotfi, F.H., Soltanifar, M.: A primal-dual method for linear programming problems with fuzzy variables. European J. of Industrial Engineering. 4, 189 (2010). https://doi.org/10.1504/EJIE.2010.031077
2. Jiménez, M., Arenas, M., Bilbao, A., Rodrı´guez, M.V.: Linear programming with fuzzy parameters: An interactive method resolution. Eur J Oper Res. 177, 1599–1609 (2007). https://doi.org/10.1016/j.ejor.2005.10.002
3. Maleki, H.R., Tata, M., Mashinchi, M.: Linear programming with fuzzy variables. Fuzzy Sets Syst. 109, 21–33 (2000). https://doi.org/10.1016/S0165-0114(98)00066-9
4. Rommelfanger, H.: A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values. Fuzzy Sets Syst. 158, 1892–1904 (2007). https://doi.org/10.1016/j.fss.2007.04.005
5. Maleki, H.R.: Ranking Functions and Their Applications to Fuzzy Linear Programming. Far East Journal of Mathematical Sciences. 283-301. . 4, 283–301 (2002)
6. Ramik, J.: Duality in Fuzzy Linear Programming: Some New Concepts and Results. Fuzzy Optimization and Decision Making. 4, 25–39 (2005). https://doi.org/10.1007/s10700-004-5568-z
7. Ganesan, K., Veeramani, P.: Fuzzy linear programs with trapezoidal fuzzy numbers. Ann Oper Res. 143, 305–315 (2006). https://doi.org/10.1007/s10479-006-7390-1
8. Nasseri, S.H., Mahmoudi, F.: A New Approach to Solve Fully Fuzzy Linear Programming Problem. Journal of Applied Research on Industrial Engineering. 6, 139–149 (2019)
9. Ezzati, R., Khorram, E., Enayati, R.: A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Appl Math Model. 39, 3183–3193 (2015). https://doi.org/10.1016/j.apm.2013.03.014
10. Edalatpanah, S.A.: A Direct Model for Triangular Neutrosophic Linear Programming . International Journal of Neutrosophic Science (IJNS). 1, 19–28 (2020)
11. Kaur, A., Kumar, A.: A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers. Appl Soft Comput. 12, 1201–1213 (2012). https://doi.org/10.1016/j.asoc.2011.10.014
12. Charnes, A., Cooper, W.W., Rhodes, E.: Measuring the efficiency of decision making units. Eur J Oper Res. 2, 429–444 (1978). https://doi.org/10.1016/0377-2217(78)90138-8
13. Tone, K.: A strange case of the cost and allocative efficiencies in DEA. Journal of the Operational Research Society. 53, 1225–1231 (2002). https://doi.org/10.1057/palgrave.jors.2601438
14. Banker, R.D., Charnes, A., Cooper, W.W.: Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Manage Sci. 30, 1078–1092 (1984). https://doi.org/10.1287/mnsc.30.9.1078
15. Zhang, G., Cui, J.: A general inverse DEA model for non-radial DEA. Comput Ind Eng. 142, 106368 (2020). https://doi.org/10.1016/j.cie.2020.106368
16. Wei, Q., Zhang, J., Zhang, X.: An inverse DEA model for inputs/outputs estimate. Eur J Oper Res. 121, 151–163 (2000). https://doi.org/10.1016/S0377-2217(99)00007-7
17. Yan, H., Wei, Q., Hao, G.: DEA models for resource reallocation and production input/output estimation. Eur J Oper Res. 136, 19–31 (2002). https://doi.org/10.1016/S0377-2217(01)00046-7
18. Hadi-Vencheh, A., Hatami-Marbini, A., Ghelej Beigi, Z., Gholami, K.: An inverse optimization model for imprecise data envelopment analysis. Optimization. 64, 2441–2454 (2015). https://doi.org/10.1080/02331934.2014.974599
19. Lertworasirikul, S., Charnsethikul, P., Fang, S.-C.: Inverse data envelopment analysis model to preserve relative efficiency values: The case of variable returns to scale. Comput Ind Eng. 61, 1017–1023 (2011). https://doi.org/10.1016/j.cie.2011.06.014
20. Farrell, M.J.: The Measurement of Productive Efficiency. J R Stat Soc Ser A. 120, 253 (1957). https://doi.org/10.2307/2343100
21. Fukuyama, H., Weber, W.L.: Estimating output allocative efficiency and productivity change: Application to Japanese banks. Eur J Oper Res. 137, 177–190 (2002)
22. Banihashem, S., Sanei, M., Mohamadian Manesh, Z.: Cost, revenue and profit efficiency in supply chain. African Journal of Business Management. 7, 4280–4287 (2013)
23. Khodabakhshi, M., Aryavash, K.: The fair allocation of common fixed cost or revenue using DEA concept. Ann Oper Res. 214, 187–194 (2014). https://doi.org/10.1007/s10479-012-1117-2
24. Mozaffari, M.R., Kamyab, P., Jablonsky, J., Gerami, J.: Cost and revenue efficiency in DEA-R models. Comput Ind Eng. 78, 188–194 (2014). https://doi.org/10.1016/j.cie.2014.10.001
25. Fang, L., Li, H.: Centralized resource allocation based on the cost–revenue analysis. Comput Ind Eng. 85, 395–401 (2015). https://doi.org/10.1016/j.cie.2015.04.018
26. Amin, G.R., Ibn Boamah, M.: A new inverse DEA cost efficiency model for estimating potential merger gains: a case of Canadian banks. Ann Oper Res. 295, 21–36 (2020). https://doi.org/10.1007/s10479-020-03667-9
27. Chen, S.-P., Hsueh, Y.-J.: A simple approach to fuzzy critical path analysis in project networks. Appl Math Model. 32, 1289–1297 (2008). https://doi.org/10.1016/j.apm.2007.04.009
28. Narayanamoorthy, S., Saranya, S., Maheswari, S.: A Method for Solving Fuzzy Transportation Problem (FTP) using Fuzzy Russell’s Method. International Journal of Intelligent Systems and Applications. 5, 71–75 (2013). https://doi.org/10.5815/ijisa.2013.02.08
29. Charles Rabinson, G., Chandrasekaran, R.: A Method for Solving a Pentagonal Fuzzy Transportation Problem via Ranking Technique and ATM. n, International Journal of Research in Engineering, IT and Social Science. 09, 71–75 (2019)
30. K.Saini, R., Sangal, A., Prakash, O.: Unbalanced Transportation Problems in Fuzzy Environment using Centroid Ranking Technique. Int J Comput Appl. 110, 27–33 (2015). https://doi.org/10.5120/19363-0998
