Input Estimation in Two-Stage Systems with Undesirable Outputs Based on Cost Efficiency
الموضوعات : International Journal of Data Envelopment Analysis
Zahra Shiri Daryani
1
(Department of Mathematics,
Islamic Azad University, South Tehran Branch,
Tehran, Iran)
Shabnam Razavyan
2
(Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran)
الکلمات المفتاحية: Network DEA, Undesirable Output, Input/output estimation, cost efficiency, Two-stage Network, Inverse DEA,
ملخص المقالة :
In the Inverse Data Envelopment Analysis (InvDEA) models, inputs and outputs of Decision Making Units (DMUs) are estimated while their relative efficiency scores remain unchanged. But, in some cases, the inputs cost information is available. This paper uses the inputs cost information and generalized the InvDEA concept in two-stage network structures with undesirable output in the second stage. To this end, it proposes a four-stage method to deal with the InvDEA concept for estimating the inputs of the DMUs with a two-stage network structure method, while the allocative efficiency scores of all units remain stable. Eventually, an empirical example is presented to illustrate the capability of the presented method.
[1] Wei, Q., Zhang, J., & Zhang, X. (2000). An inverse DEA model for inputs/outputs estimate. European Journal of Operational Research, 121(1), 151–163.
[2] 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.
[3] Jahanshahloo, G. R., Lotfi, F. H., Shoja, N., Tohidi, G., & Razavyan, S. (2004a). The outputs estimation of a DMU according to improvement of its efficiency. Applied Mathematics and Computation, 147(2), 409–413.
[4] Hadi-Vencheh, A., Foroughi, A.A., (2006). A generalized DEA model for inputs/outputs estimation, Mathematical and Computer Modeling, 43, 447-457.
[5] 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 & Industrial Engineering, 61, 1017–1023.
[6] Eyni, M., Tohidi, G., Mehrabian, S., (2016). Applying inverse DEA and cone constraint to sensitivity analysis of DMUs with undesirable inputs and outputs, Journal of the Operational Research Society, 68 (1), 34-40.
[7] Ghiyasi, M., (2017b). Industrial sector environmental planning and energy efficiency of Iranian provinces, 142 (4), 2328-2339.
[8] An, Q., Liu, X., Li, Y., Xiong, B., (2019), Resource planning of Chinese commercial banking systems using two stage, PLoS ONE, 14 (6), e0218214.
[9] Hu, X., Li, J., Li, X., Cui, J., (2020). A revised inverse data envelopment analysis model based on radial models, Mathematics, 8, 803.
[10] Ghobadi, S. (2018). Inverse DEA using enhanced Russell measure in the presence of fuzzy data. Int. J. Ind. Math., 10, 165–180.
[11] Zhang, G., Cui, J., (2020), A general inverse DEA model for non-radial DEA, Computer and Industrial Engineering, 142.
[12] Emrouznejad, A.,Yang, G., Amin, G.R., (2019). A novel inverse DEA model with application to allocate the CO2 emissions quota to different regions in Chinese manufacturing industries, Journal of the Operational Research Society, 70 (7), 1079-1090.
[13] 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.
[14] Chen, Y., Chen, M., Li, T., (2021). China's CO2 emissions reduction potential: A novel inverse DEA model with frontier changes and comparable value. Energy Strategy Reviews, 38, 100762.
[15] Gattoufi, S., Amin, G. R., & Emrouznejad, A., (2014). A new inverse DEA method for merging banks. IMA Journal of Management Mathematics, 25(1), 73–87.
[16] Amin, G.R., Emrouznejad, A., Gattoufi, S., (2017). Minor and major consolidations in inverse DEA: Definition and Determination, Computers & Industrial Engineering 103, 193–200.
[17] Amin, G.R., Al-Muharrami, S., (2016). A new inverse data envelopment analysis model for mergers with negative data, MA Journal of Management Mathematics, 29 (2), 137–149.
[18] Hassanzadeh, A., Yousefi., S., Farzipour Saen, R., Seyed Hosseininia, S, S., (2018). How to assess sustainability of countries via inverse data envelopment analysis? Clean Technologies and Environmental Policy, 20, 29-40.
[19] 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.
[20] Soltanifar, M., Ghiyasi, M., Sharafi, H. (2022a). Inverse DEA-R models for merger analysis with negative data. IMA Journal of Management Mathematics, 00, 1-20.
[21] Amin, G.R., Al-Muharrami, S., Mehdi Toloo, M., (2019). A combined goal programming and inverse DEA method for target setting in mergers, Expert Systems with Applications, 115, 412-417.
[22] 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.
[23] Soltanifar, M., Ghiyasi, M., Emrouznejad, A., Sharafie, H., (2022b). A Novel Model for Merger Analysis and Target Setting: A Csw-Inverse DEA Approach. Available at SSRN 4115552.
[24] Seiford, L.M., Zhu, J., (1999). Profitability and Marketability of the Top 55 US Commercial Banks.”Management Science, 45, 1270-1288.
[25] Farrell, M.J., (1957). The measurement of productive efficiency, Journal of the Royal Statistical Society Series A, 120 (3), 253 – 281.
[26] Wang, Q., Wu, Z., Chen, X., (2019). Decomposition weights and overall efficiency in a two-stage DEA model with shared resources, Computers & Industrial Engineering, 136, 135-148.
[27] Wang, Y., Pan, J.F., Pie, R.M., Yi, B. W., Yang, G. L., (2020). Assessing the technological innovation efficiency of China’s high-tech industries with a two-stage network DEA approach, Socio-Economic Planning Sciences, In Press.
[28] Lozano, S., (2011), Scale and cost efficiency analysis of networks of processes, Expert Systems with Applications, 38, 6612–6617.
[29] Shi, X., Li, Y., Emrouznejhad, A., Xie, J., Liang. L., (2017). Estimation of potential gains from bank mergers: a novel two stage cost efficiency DEA model, Journal of the operational research society, 68, 1045-1055.
[30] Shiri Daryani, Z., Tohidi, G., Daneshian, B., Razavyan, Sh., Hosseinzadeh Lotfi, F., (2021). Inverse DEA in Two-Stage Systems Based on Allocative Efficiency, Journal of Intelligent and Fuzzy Systems, 40, 591-603.
[31] Ghiyasi, M., (2017a). Inverse DEA based on cost and revenue efficiency, Computers & Industrial Engineering, 114, 258–263.
[32] Soleimani-Chamkhorami, Kh., Hosseinzade Lotfi, F., Jahanshahloo, G. R., Rostamy-Malkhalifeh, M., (2019a), Preserving cost and revenue efficiency through inverse data envelopment analysis models, Information Systems and Operational Research, 1-18.
[33] Soleimani-Chamkhorami, Kh., Hosseinzade Lotfi, F., Jahanshahloo, G. R., Rostamy-Malkhalifeh, M., (2019b), A ranking system based on inverse data envelopment analysis, Journal of Management Mathematics, 1-19.
[34] Kalantary, M., Farzipoor Saen, R., Toloie Eshlaghy, A., (2018a). Sustainability assessment of supply chains by inverse network dynamic data envelopment analysis, Scientia Iranica, 25(6), 3723-3743.
[35] Kalantary, M., Farzipoor Saen, R., Toloie Eshlaghy, A., (2018b). Assessing Sustainability of Supply Chains: An Inverse Network Dynamic DEA Model, Computers & Industrial Engineering, 135, 1224-1238.
[36] Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.
[37] Ghiyasi, M. (2015). On inverse DEA model: The case of variable returns to scale. Computers & Industrial Engineering, 87, 407–409.
[38] Steuer, R.E., (1986). Multiple Criteria Optimization: Theory, Computation, and Application. Krieger Publishing, Malabar, FL.
