Fixed Cost Allocation Based on DEA Cross Efficiency Considering Semi-Additive Production Technology: An Application to Bank Branches
الموضوعات :
1 - Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
الکلمات المفتاحية: Semi-additive production technology, Banking, Data envelopment analysis, Fixed cost allocation,
ملخص المقالة :
In the real world, situations frequently occur when we want to allocate a fixed cost between a set of decision-making units (DMUs) such as institutions, organizations. In this paper, we use the data envelopment analysis (DEA) technique to allocate fixed costs among DMUs. First, we introduce semi-additive production technology in DEA and present efficiency evaluation models in this technology. In estimating the frontier of this technology, in addition to the observed DMUs, the set of all aggregations of these DMUs are also used. In the following, we propose an interactive process for fixed cost allocation between DMUs in DEA based on the concept of cross-efficiency. We show that our proposed iterative approach is always feasible, and ensures that all DMUs become efficient after the fixed cost is allocated as an additional input measure. The cross-efficiency scores corresponding to all DMUs are improved at each stage of the interactive process. We also illustrate the proposed approach with a numerical example. The proposed approaches are demonstrated using an application of the fixed cost allocation problem for branches of commercial banks. Finally, we bring the results of the research.
[1] An, Q. X., Wang, P., Shi, S. S., Fixed cost allocation for two-stage systems with cooperative relation-ship using data envelopment analysis, Computers and Industrial Engineering, 2020; 145: 106534. doi: 10.1016/j.cie.2020.106534.
[2] An, Q., Wang, P., Emrouznejad, A., Hu, J., Fixed cost allocation based on the principle of efficiency invariance in two-stage systems, European Journal of Operational Research, 2020; 283(2): 662-675. doi: 10.1016/j.ejor.2019.11.031.
[3] Banker, R.D., Charnes, A., Cooper, W.W., Some models for estimating technical and scale inefficien-cies in
data envelopment analysis, Management Science, 1984; 30: 1078-1092. doi:10.1287/mnsc.30.9.1078.
[4] Beasley, J. E., Allocating fixed costs and resources via data envelopment analysis, European Journal of Operational Research, 2003; 147(1): 198–216. doi: 10.1016/s0377-2217(02)00244-8.
[5] Charnes, A., Cooper, W.W., Rhodes, E., Measuring the efficiency of decision-making units, European Journal of Operational Research, 1978; 2(6):429–444. doi: 10.1016/0377-2217(78)90138-8.
[6] Chu, J. F., Wu, J., Chu, C. B., Zhang, T. L., DEA-based fixed cost allocation in two-stage systems: Leader-follower and satisfaction degree bargaining game approaches, 2020; Omega :94. doi: 10.1016/j.omega.2019.03.012.
[7] Cook, W. D., Kress, M., Characterizing an equitable allocation of shared costs: A DEA approach, Eu-ropean Journal of Operational Research, 1999; 119 (3): 652–661. doi: 10.1016/s0377-2217(98)00337-3.
[8] Cook, W. D., Zhu, J., Allocation of shared costs among decision making units: a DEA approach, Com-puters and Operations Research, 2005; 32(8): 2171–2178. doi: 10.1016/j.cor.2004.02.007.
[9] Deprins, D., Simar, L., Tulkens, H., Measuring labor-efficiency in post offices. Public goods, environ-mental externalities and fiscal competition, Springer, 2006. doi: 10.1007/978-0-387-25534-7-16.
[10] Du, J., Cook, W. D., Liang, L., Zhu, J., Fixed cost and resource allocation based on DEA cross-efficiency, European Journal of Operational Research, 2014; 235(1): 206–214. doi: 10.1016/j.ejor.2013.10.002.
[11] Fare, R., Grosskopf, S., Lovell, C.A.K., The Measurement of Efficiency of Production, Kluwer Aca-demic Publisher,Boston, MA, 1985.
[12] Feng, Q., Wu, Zh., Zhou, G., Fixed cost allocation considering the input-output scale based on DEA approach, Computers & Industrial Engineering, 2021; 159: 107476. doi:10.1016/j.cie.2021.107476.
[13] Ghiyasi M., A DEA production technology and its usage for incorporation of collaboration in effi-ciency analysis: an axiomatic approach, International Transactions in Operational Research, 2016; 26:1118–34. doi: 10.1111/itor.12325.
[14] Ghiyasi M., Cook W.D., Modelling the semi-additive production technology in DEA, Omega, 2021; 103: 102385. doi: 10.1016/j.omega.2020.102385.
[15] Green, R.H., Cook, W.D., A free coordination hull approach to efficiency measurement, Journal of the Operational Research Society, 2004; 55: 1059–1063. doi: 10.1057/palgrave.jors.2601773.
[16] Grosskopf, S., The role of the reference technology in measuring productive efficiency, The Econom-ic Journal, 1986; 96: 499–513. doi: 10.2307/2233129.
[17] Izadikhah, M., Financial Assessment of Banks and Financial Institutes in Stock Exchange by Means of an Enhanced Two stage DEA Model, Advances in Mathematical Finance and Applications, 2021; 6(2): 207-232. doi: 10.22034/amfa.2020.1910507.1491.
[18] Koopmans, T.C., Examples of production relations based on micro data, In Harcourt, G.C. (ed.) The Microeconomic Foundations of Macroeconomic. Palgrave Macmillan, Basingstoke, 1977; 144–178. doi: 10.1007/978-1-349-03236-5-6.
[19] Li, Y. J., Yang, M., Chen, Y., Dai, Q., Liang, L., Allocating a fixed cost based on data envelopment analysis and satisfaction degree, Omega, 2013; 41(1): 55–60. doi: 10.1016/j.omega.2011.02.008.
[20] Li, Y. J., Li, F., Emrouznejad, A., Liang, L., Xie, Q. W., Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game. Annals of Operations Research, 2019; 274(1): 373–394. doi: 10.1007/s10479-018-2860-9.
[21] Li, F., Zhu, Q., Liang, L., Allocating a fixed cost based on a DEA-game cross efficiency approach, Expert Systems with Applications, 2018; 96:196–207. doi: 10.1016/j.eswa.2017.12.002.
[22] Mozaffari, M. M., Ghasemi, M., Hosseinzadeh Lotfi, F., Rostamy-Malkhalifeh, M., Behzadi, M.H., A New Method for Allocating Fixed Costs with Undesirable Data: Data Envelopment Analysis Approach. Advances in Mathematical Finance and Application. doi:10.22034/amfa.2022.1915270.1514.
[23] Tohidi, G., Tohidnia, S., Measuring the Interval industry cost efficiency score in DEA, Advanc-es in Mathematical Finance and Applications, 2022; 7(2): 379-390. doi:10.22034/amfa.2020.1880449.1308.
