Quarterly Publication

Document Type : Research Paper

Authors

1 Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran.

2 Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.

Abstract

Sensitivity analysis in optimization problems is important for managers and decision maker to introduce different strategies. Data Envelopment Analysis (DEA) is a method based on mathematical programming to evaluate the efficiency of a set of Decision-Making Units (DMUs). Due to the importance of sensitivity analysis in an optimization problem, a development of DEA model called inverse model in DEA is presented. The purpose of this model is to analyze the sensitivity of some inputs or outputs to changes in some other inputs or outputs of the unit under evaluation, provided that the amount of efficiency remains constant or improves at the discretion of the manager. In this research, for the first time, we introduce the inverse model in DEA with network structure. In fact, we examine the extent to which the input parameters are likely to change based on the presuppositions of the problem, for the output changes that are applied as the manager desires. One of the key points of this research is that to make the modeling more consistent with reality, the leader-follower method was used in estimating the parameters in the network. In addition, the opinions of the system manager and the decision maker, who have full control over the system under their management, are included in this modeling to estimate the desired values. Another feature of this modeling is the consideration of uncontrollable factors in the inverse model in DEA with network structure. Finally, using a numerical example, the results obtained are analyzed based on the proposed model.

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Main Subjects

###### ##### References
[1]     Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429–444.
[2]     Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078–1092.
[3]     Gatimbu, K. K., Ogada, M. J., & Budambula, N. L. M. (2020). Environmental efficiency of small-scale tea processors in Kenya: an inverse data envelopment analysis (DEA) approach. Environment, development and sustainability, 22(4), 3333–3345. DOI:10.1007/s10668-019-00348-x
[4]     Emrouznejad, A., & Yang, G. L. (2018). A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-economic planning sciences, 61, 4–8. DOI:10.1016/j.seps.2017.01.008
[5]     Kaffash, S., Azizi, R., Huang, Y., & Zhu, J. (2020). A survey of data envelopment analysis applications in the insurance industry 1993–2018. European journal of operational research, 284(3), 801–813.
[6]     Kao, C. (2017). Network data envelopment analysis. Springer.
[7]     Fare, R., & Grosskopf, S. (2000). Network DEA. Socio-economic planning sciences, 34(1), 35–49.
[8]     Wei, Q., Zhang, J., & Zhang, X. (2000). An inverse DEA model for inputs/outputs estimate. European journal of operational research, 121(1), 151–163. DOI:10.1016/S0377-2217(99)00007-7
[9]     Yan, H., Wei, Q., & Hao, G. (2002). DEA models for resource reallocation and production input/output estimation. European journal of operational research, 136(1), 19–31.
[10]   Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Shoja, N., Tohidi, G., & Razavyan, S. (2004). The outputs estimation of a DMU according to improvement of its efficiency. Applied mathematics and computation, 147(2), 409–413. DOI:10.1016/S0096-3003(02)00734-8
[11]   Hadi-Vencheh, A., Foroughi, A. A., & Soleimani-Damaneh, M. (2008). A DEA model for resource allocation. Economic modelling, 25(5), 983–993.
[12]   Lertworasirikul, S., Charnsethikul, P., & Fang, S. C. (2011). Inverse data envelopment analysis model to preserve relative efficiency values: the case of variable returns to scale. Computers and industrial engineering, 61(4), 1017–1023. DOI:10.1016/j.cie.2011.06.014
[13]   Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Rostamy-Malkhalifeh, M., & Ghobadi, S. (2014). Using enhanced Russell model to solve inverse data envelopment analysis problems. The scientific world journal, 2014. https://www.hindawi.com/journals/tswj/2014/571896/
[14]   Mirsalehy, A., Bakar, M. R. A., Lee, L. S., Jaafar, A. B., & Heydar, M. (2014). Directional slack-based measure for the inverse data envelopment analysis. The scientific world journal, 2014, 1–9.
[15]   Ghiyasi, M. (2015). On inverse DEA model: The case of variable returns to scale. Computers and industrial engineering, 87, 407–409. DOI:10.1016/j.cie.2015.05.018
[16]   Hadi-Vencheh, A., Hatami-Marbini, A., Ghelej Beigi, Z., & Gholami, K. (2015). An inverse optimization model for imprecise data envelopment analysis. Optimization, 64(11), 2441–2454.
[17]   Ghiyasi, M. (2017). Inverse DEA based on cost and revenue efficiency. Computers and industrial engineering, 114, 258–263. DOI:10.1016/j.cie.2017.10.024
[18]   Ghobadi, S. (2018). Inverse DEA using enhanced Russell measure in the presence of fuzzy data. International journal of industrial mathematics, 10(2), 165–180.
[19]   Amin, G. R., & Ibn Boamah, M. (2021). A two-stage inverse data envelopment analysis approach for estimating potential merger gains in the US banking sector. Managerial and decision economics, 42(6), 1454–1465. DOI:10.1002/mde.3319
[20]   Wegener, M., & Amin, G. R. (2019). Minimizing greenhouse gas emissions using inverse DEA with an application in oil and gas. Expert systems with applications, 122, 369–375.
[21]   Ghiyasi, M., & Khoshfetrat, S. (2019). Preserve the relative efficiency values: An inverse data envelopment analysis with imprecise data. International journal of procurement management, 12(3), 243–257.
[22]   Ghiyasi, M., & Zhu, N. (2020). An inverse semi-oriented radial data envelopment analysis measure for dealing with negative data. IMA journal of management mathematics, 31(4), 505–516.
[23]   Gerami, J., Mozaffari, M. R., Wanke, P. F., & Correa, H. L. (2023). A generalized inverse DEA model for firm restructuring based on value efficiency. IMA journal of management mathematics, 34(3), 541–580. DOI:10.1093/imaman/dpab043