International Journal of Finance & Managerial Accounting

International Journal of Finance & Managerial Accounting

Designing a data envelopment analysis model with a network structure and undesirable output for allocating fixed costs in bank branches

Document Type : Review paper

Authors
leila taghizade tame 1
farhad hosseinzadeh lotfi 2
Mohsen Rostamy Malkhalifeh 2
1 Ph.D. Student, Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 Ph.D., Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
10.30495/ijfma.2024.69818.1930
Abstract
The fixed cost allocation in bank branches by supervisors or central headquarters has always been the concern of managers and researchers. In numerous operative applications, the units under assessment or evaluation are in a combined form, such as, mixed, in series and parallel units; and correspondingly, of an undesirable output. in this paper, we have initially presented a mixed network assessment model, with an independent input and a common intermediate, along with, an undesirable output. Subsequently, with due attention to the significance of the fixed cost allocation in relevance with mixed networks, a model for the fixed cost allocation, has been rendered, in context to the intermediate input, such that, the overall efficiency and the efficiency of the sub-units of the network do not deteriorate further, to the most probable extent after allocation, but rather, enhance to the utmost possible degree. So as to achieve an exceptional and exclusive value, a secondary goal has been taken advantage of; and this procedure, condenses the possibility of varied solutions. Likewise, CSW technique has been utilized for assessment purposes in the paper, which provides accurate results compared to the results obtained from classical models. The model proposed in this paper is ultimately implemented in an empirical example with 50 branches of one of Iran's commercial banks. the results of which, presents an example of a fair allocation, such that, the total efficiency, as well as the efficiency of the sub-units, refrain from decrease and increase as much as possible, after the allocation.
Keywords
Fixed Cost Allocation
Data Envelopment Analysis (DEA) Network
Mixed Network
Undesirable Output and Common set of Weights
[1] Amirteimoori, A., Kordrostami, S., Sarparast, M. (2006). Modeling undesirable factors in data envelopment analysis. Applied Mathematics and Computation. 180 (2) 444–452.
[2] An, Q., Wang, P., Shi, S., (2020). Fixed cost allocation for two-stage systems with cooperative relationship using data envelopment analysis. Computers & Industrial Engineering 145- 106534.
[3] An, Q.  Wang, P., Yang, H., Wang, Z.- (2021). Fixed cost allocation in two-stage system using DEA from a non-cooperative view. OR Spectrum. 1-26.
[4] An, Q., Wen, Y., Ding, T., Li, Y. (2019). Resource sharing and payoff allocation in a three-stage system: Integrating network DEA with the Shapley value method, Omega, 85-16-25
[5] Beasley, J. E. (2003) Allocating fixed costs and resources via data envelopment analysis. European Journal of Operational Research. 147(1)198–216.
[6] Charnes, A., Cooper, W. W., Rhodes, E. (1978) Measuring the Efficiency of Decision-Making Units, European Journal of Operational Research, 2(6) 429–444.
[7] Chen, Y., Liang, L., Zhu, J., (2009). Equivalence in Two-Stage DEA Approaches. European Journal of Operational Research, 193(2)600–4.
[8] Chen, Y., Zhu, J. (2004).  Measuring information technology sin direct impact on firm performance. Information Technology & Management Journal. 5(1-2)9–22.
[9] Cook, W. D., Kress, M. (1990). Data envelopment model for aggregating preference ranking. Management Science, 36(11), 1302–1310   
[10] Cook, W. D., Kress, M. (1999) Characterizing an equitable allocation of shared costs: a dea approach. European Journal of Operational Research, 119(3)652–661.
[11] Cook, W. D., Zhu J (2005) Allocation of shared costs among decision making units: a dea approach. Computers & Operations Research32(8)2171–2178
[12] Chu, J., Wu, J ., Chu, C., Zhang,T. (2020). DEA-based fixed cost allocation in two-stage systems: leader-follower and satisfaction degree bargaining game approaches. Omega.94-102054
[13] Davoodi, A., Zhiani Rezai, H. (2012). Common set of weights in  data envelopment analysis: a linear programming problem. Central European Journal of Operational Research, 20(2) 355–365.
[14] Ding, T., Ya Chen, Huaqing Wu Yuqi Wei. (2017). Centralized fixed cost and resource allocation considering technology heterogeneity: a DEA approach. Annals of Operations Research. 268(1) 497-511
[15] Ding, T., Zhu, Q., Zhang, B., Liang, L. (2019). Centralized fixed cost allocation for generalized two-stage network DEA. INFOR: Information Systems and Operational Research57(2) 123-140.
[16] Qianzhi Dai, Yongjun Li, Xiyang Lei, Dengsheng Wu. (2020). A DEA-based incentive approach for allocating common revenues or fixed costs.
[17] Du, J., Cook, W.D., Liang, L., Zhu, J. (2014). Fixed cost and resource allocation based on DEA cross-efficiency. European Journal of Operational Research, 235(1)206–214
[18] Farrell, M. J., (1957) The Measurement of Productive Efficiency, Journal of the Royal Statistical Society, Series A, General120, pp. 253–281.
 [19] Li, F., Zhu, Q., Liang, L. (2018). Allocating a fixed cost based on a DEA-game cross efficiency approach. Expert Systems with Applications, 96, 196-207.
[20] Li, F., Zhu, Q., Liang, L. (2019). A new data envelopment analysis based approach for fixed cost allocation Annals of Operations Research, 274(1) 347-372.
[21] Feng, Q., Wu, Z., Zhou, G. (2021) Fixed cost allocation considering the input-output scale based on DEA approach. Computers & Industrial Engineering, 159 -107476.
[22] Halkos, G., Papageorgiou, G. (2014). Spatial environmental efficiency indicators in regional waste generation: A nonparametric approach, Journal of Environmental Planning and Management, 59(1) 62-78.
[23] Halkos, G.E., Polemis, M.L., (2018). The impact of economic growth on environmental efficiency of the electricity sector: A hybrid window DEA methodology for the USA. Journal of Environmental Planning and Management. 211, 334–346
[24] Halkos, G., Tzeremes, N., (2013). An additive two-stage DEA approach creating sustainability efficiency indexes. MPRA.
[25] Jahanshahloo, G. R., Lotfi, F. H., Shoja, N., Sanei, M. (2004) An alternative approach for equitable allocation of shared costs by using dea. Appl Math Comput 153(1)267–274
[26] Jahanshahloo, G.R., Lotfi, F.H., Shoja, N., Tohidi, G., Razavyan, S., (2005). Undesirable inputs and outputs in DEA models. Appl. Math. Comput. 169 (2), 917–925.
[27] Sun, J., Chen, M., Fu, Y., Luo, H. (2021). Allocating fixed resources for DMUs with interval data. RAIRO-Operations Research. 55(2) 505-520.
[28] Kao. C, Hwang. S. N. (2008). Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan. European Journal of Operational Research,185(1)418–29.
[29] Lin. R. (2011a). Allocating fixed costs or resources and setting targets via data envelopment analysis. Applied Mathematics and Computation, 217(13)6349–6358.
[30] Lin, R. (2011b). Allocating fixed costs and common revenue via data envelopment analysis. Applied Mathematics and Computation, 218(7)3680–3688.0
[31] Lin. R., Chen. Z. (2020). A DEA‐based method of allocating the fixed cost as a complement to the original input. International Transactions in Operational.27(4) 2230-2250.
[32] Li. Y., Yang. M., Chen. Y., Dai. Q, Liang. L. (2013). Allocating a fixed cost based on data envelopment analysis and satisfaction degree. Omega 41(1)55–6
[33] Li. Y., Yang. F., Liang. L., Hua. Z. (2009). Allocating the fixed cost as a complement of other cost inputs. a dea approach. European Journal of Operational Research. 197(1)389–401.  
[34] Li. F., Zhu.Q., Chen.Z. (2019). Allocating a fixed cost across the decision making units with two-stage network structures. Omega. 83 (2019) 139–154
 [35] Lotfi. F. H., Hatami-Marbini. A, Agrell. P. J., Aghayi. N., Gholami. K. (2013). Allocating fixed resources and setting targets using a common-weights dea approach. Computers Industrial Engineering. 64(2)631–640.
[36] Mohd. S. A., Khan. N., Ramli. R., Azizul Baten. M. D. (2015). Enhanced DEA model with undesirable output and interval data for rice growing farmers performance assessment. AIP Conference Proceedings.  1691(1) 30016.
[37] Seiford. L. M., Zhu. J., (1999). Profit ability and market ability of the top 55US commercial banks. Management Science. 45(9)1270–88.
[38] Xiong. B., Wu. J., An. Q., Chu. J., Liang. L. (2018). Resource allocation of a parallel system with interaction consideration using a DEA approach: an application to Chinese input–output table. INFOR: Information Systems and Operational Research 56(3)298-316.
[39] Yu. MM., Chen. LH., Hsiao. B. (2016). A fixed cost allocation based on the two-stage network data envelopment approach, Journal of Business Research. 69 (5) 1817–1822.
[40] Yang, H., Pollitt, M. (2009). Incorporating both undesirable outputs and uncontrollable variables into DEA: The performance of Chinese coal-fired power. European journal of operational research. 197(3) 1095-1105.
[41] Zanella, A. (2014). Assessment of performance in the presence of undesirable outputs: the promotion of livability and sustainable development of cities and countries using Data Envelopment Analysis. In: Ph.D. thesis
[42] Zhu.W., Zhang.Q., H Wang.H. (2019) Fixed costs and shared resources allocation in two-stage network DEA. Annals of Operations Research. 278(1-2) 177-