Fixed cost allocation in bank branches: A network DEA approach

Document Type : Original Article

Authors

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

10.30495/ijfma.2022.67669.1864

Abstract

Data Envelopment Analysis (DEA) approach is a mathematical method of exploring homogeneous decision-making units (DMUs). The structure of DMUs may have multiple steps, where one of the steps employs the output of another as its input. Manufacturing operations and industrial systems, in particular, use multi-stage structures. This study addresses the topic of constant cost distribution in a specific type of two-stage system. First, a set of common weights and sized-based allocations are performed. Eventually, a min-max approach is established to decrease the difference between efficient and size-based allocations. Researching banking issues is very important because banks can highly affect the economic growth of countries.The proposed method for determining fixed cost allocation in bank branches has been performed on 37 branches of Iranian banks.The fixed cost was allocated based on the aggregate of inputs and outputs of the bank branches and all DMUs and subphases became efficient after fixed cost allocation.

Keywords


  • Abdali E, Fallahnejad R. A bargaining game model for measuring efficiency of two-stage network DEA with non-discretionary inputs. International Journal of Computer Mathematics: Computer Systems Theory 2020;5(1):48-59.
  • Alinezhad A. Combination of DEA and ANP-QUALIFLEX Methods to determine the most Efficient Portfolio (Case study: Tehran Stock Exchange). International Journal of Finance and Managerial Accounting 2018; 3(9): 79-90
  • Amirteimoori A, Kordrostami S. Allocating fixed costs and target setting: a DEA-based approach. Applied Mathematics and Computation 2005;171(1):136–51.
  • Amirteimoori A, Tabar MM. Resource allocation and target setting in data envelopment analysis. Expert Systems with Applications 2010;37(4):3036–9.
  • 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): 662-657.
  • An Q, Wang P, Shi S . Fixed cost allocation for two-stage systems with cooperative relationship using data envelopment analysis. Computers & Industrial Engineering 2020;145:106-534.
  • An Q, Wang P, Yang H,  Wang Z . Fixed cost allocation in two-stage system using DEA from a noncooperative view.OR Spectrum 2021;43:1077-1102.
  • Ashrafi J, Banimahd B,  Nikoomaram H. The Ranking of Corporate Social Responsibility by Using of DEA Cross Efficiency. International Journal of Finance and Managerial Accounting 2018; 3(11): 11-22.
  • Banker RD, Charnes A, Cooper WW. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 1984;30(9):1078–92.
  • Beasley JE. Allocating fixed costs and resources via data envelopment analysis. European Journal of Operational Research 2003;147(1):198–216.
  • Bi G, Ding J, Luo Y, Liang L. Resource allocation and target setting for parallel production system based on DEA. Applied Mathematical Modelling 2011;35(9):4270–80.
  • Bian Y, Liang N, Xu H . Efficiency evaluation of Chinese regional industrial systems with undesirable factors using a two-stage slacks-based measure approach. Journal of Cleaner Production 2015;87:348–56.
  • Charnes A, Cooper WW. Programming with linear fractional functional. Naval Research Logistics 1962;9(3-4):181–6 .
  • Charnes A, Cooper WW, Rhodes E . Measuring the efficiency of decision-making units. European Journal of Operational Research 1978;2(6):429–44.
  • Chen Y, Cook WD, Li N, Zhu J . Additive efficiency decomposition in two-stage DEA. European Journal of Operational Research 2009a;196(3):1170–6.
  • Chen Y, Du J, Sherman HD, Zhu J . DEA model with shared resources and efficiency decomposition. European Journal of Operational Research 2010;207(1):339–49.
  • Chen Y, Liang L, Zhu J . Equivalence in two-stage DEA approaches. European Journal of Operational Research 20 09b;193(2):60 0–4.
  • Chu J, Jiang H. Fixed cost allocation based on the utility: A DEA common-weight Approach. IEEE Access 2019;7:72613-72621.
  • Chu J, Wu J, Chu C, Zhang T. DEA-based fixed cost allocation in two-stage systems: leader-follower and satisfaction degree bargaining game approaches. Omega 2020;94:102054
  • Cook WD, Kress M. Characterizing an equitable allocation of shared costs: a DEA approach. European Journal of Operational Research 1999;119(3):652–61.
  • Cook WD, Liang L, Zhu J . Measuring performance of two-stage network structures by DEA: a review and future perspective. Omega 2010;38(6):423–30.
  • Cook WD, Zhu J . Allocation of shared costs among decision-making units: A DEA approach. Computers & Operations Research 2005;32(8):2171–8.
  • Ding T, chen Y, Wu H, Wei Y. Centralized fixed cost and resource allocation considering technology heterogeneity: A DEA approach. Annals of Operations  Research 2018;268(1-2):497-511.
  • Ding T, Zhu Q, Zhang B, Liang L. Centralized fixed cost allocation for generalized two-stage network DEA. INFOR: Information Systems and Operational Research 2019;57(2):123-140
  • Ding T, Li F, Liang L. Fixed Cost and Resource Allocation Considering technology heterogeneity in two-stage network production systems. Data Science and Productivity Analytics 2020; 227-249.
  • Du J., Cook WD, Liang L, Zhu J. Fixed cost and resource allocation based on DEA cross-efficiency. European Journal of Operational Research 2014;235(1):206–14.
  • Du J, Liang L, Chen Y, Cook WD, Zhu J. A bargaining game model for measuring performance of two-stage network structures. European Journal of Operational Research 2011;210(2):390–7.
  • Emrouznejad A, Parker BR, Tavares G . Evaluation of research in efficiency and productivity: a survey and analysis of the first 30 years of scholarly literature in DEA. Socio-Economic Planning Sciences 2008;42(3):151–7.
  • Emrouznejad A, Yang GL. A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-Economic Planning Sciences 2018; 61:4–8.
  • Fukuyama H, Matousek R . Modelling bank performance: A network DEA approach. European Journal of Operational Research 2017;259(2):721–32.
  • Hadi-Vencheh A, Ghelej Beigi Z, Gholami K. The allocation of sub decision making units to parallel fuzzy network systems. Kybernetes 2014;43(7):1079–97.
  • Hosseinzadeh LotfiF, Hatami-Marbini A, Agrell PJ, Aghayi N, Gholami K. Al- locating fixed resources and setting targets using a common-weights DEA approach. Computers & Industrial Engineering 2013;64(2):631–40.
  • Hosseinzadeh LotfiF, Jahanshahloo GR, Allahviranloo T, Noroozi E, Hossein zadeh LotfiAA. Equitable allocation of shared costs on fuzzy environment. International Mathematical Forum 2007;2(65):3199–210.
  • Jahanshahloo GR, LotfiFH, Shoja N, Sanei M. An alternative approach for equitable allocation of shared costs by using DEA. Applied Mathematics and Computation 2004;153(1):267–74.
  • Jahanshahloo GR, Sadeghi J, Khodabakhshi M. Proposing a method for fixed cost allocation using DEA based on the efficiency invariance and common set of weights principles. Mathematical Methods of Operations Research 2017;85(2):223–40 .
  • Kaffash S, Marra M. Data envelopment analysis in financial services: A citations network analysis of banks, insurance companies and money market funds. Annals of Operations Research 2017; 253(1): 307–344.
  • Kao C, Hwang SN. Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan. European Journal of Operational Research 2008;185(1):418–29.
  • Khodabakhshi M, AryavashK. The fair allocation of common fixed costor revenue using DEA concept. Annals of Operations  Research 2014;214(1):187–94.
  • Liang L, Cook WD, Zhu J . DEA models for two-stage processes: game approach and efficiency decomposition. Naval Research Logistics 2008;55(7):643–53.
  • Li F, Liang L, Li Y, Emrouznejad A. An alternative approach to decompose the potential gains from mergers. Journal of Operational Research Society 2018a doi: 10.1080/01605682.2017. 1409867.
  • Li F, Song J, Dolgui A, Liang L. Using common weights and efficiency invariance principles for resource allocation and target setting. International Journal of Production Research 2017a;55(17):4982–97.
  • Li F, Yan Z, Zhu Q, Yin M, Kou G. Allocating a fixed cost across decision making units with explicitly considering efficiency rankings. Journal of the Operational Research Society 2021; 72:1432-1446.
  • Li F, Zhu Q, Chen Z. Allocating a fixed cost across the decision making units with two-stage network structures. Omega (2018), doi:10.1016/j.omega.2018.02.009
  • Li F, Zhu Q, Chen Z. (2018b). Allocating a fixed cost across the decision making units with two-stage network structures. Omega 2019;83:139-154.
  • Li F, Zhu Q, Liang L. Allocating a fixed cost based on a DEA-game cross efficiency approach. Expert Systems with Applications 2018b;96:196–207.
  • Li F, Zhu Q, Liang L. A new data envelopment analysis based approach for fixed cost allocation. Annals of Operations  Research 2019;274(1-2):347-372.
  • Li F, Zhu Q, Zhuang J . Analysis of fire protection efficiency in the United States: a two-stage DEA based approach. OR Spectrum 2018;40(1):23–68.
  • [48] Li H, Chen C, Cook WD, Zhang J, Zhu J . Two-stage network DEA: who is the leader. Omega 2017b;74:15–19.
  • [49] Li Y, Chen Y, Liang L, Xie J . DEA models for extended two-stage network structures. Omega 2012;40(5):611–18.
  • [50] Li Y, Li F, Emrouznejad A, Liang L, Xie Q. Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game. Annals of Operations Research 2019;274(1-2):373-394.
  • [51] Li Y, Yang F, Liang L, Hua Z. Allocating the fixed cost as a complement of other cost inputs: A DEA approach. European Journal of Operational Research 2009;197(1):389–401.
  • [52] Li Y, 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.
  • [53] Lin R . Allocating fixed costs or resources and setting targets via data envelopment analysis. Applied Mathematics and Computation 2011a;217(13):6349–58.
  • [54] Lin R . Allocating fixed costs and common revenue via data envelopment analysis. Applied Mathematics and Computation 2011b;218(7):3680–8.
  • [55] Lin R, Chen Z. A DEA-based method of allocating the fixed cost as a complement to the original input. International Transactions in Research 2020;27(4):2230-2250.
  • [56] Lin R, Chen Z. Fixed input allocation methods based on super CCR efficiency invariance and practical feasibility. Applied Mathematical Modelling 2016;40(9):5377–92.
  • [57] Maghbouli M, Amirteimoori A, Kordrostami S. Two-stage network structures with undesirable outputs: A DEA-based approach. Measurement 2014;48:109–18.
  • [58] Meng F, Wu Li, Chu Junfei. Allocating the fixed cost based on data envelopment analysis in view of the Shapley value. Expert Systems 2020;e12539.
  • [59] Moreno P, Lozano S. A network DEA assessment of team efficiency in the NBA. Annals of Operations  Research 2014;214(1):99–124.
  • [60] Mostafaee A . An equitable method for allocating fixed costs by using data envelopment analysis. Journal of Operational Research Society 2013;64(3):326–35 .
  • [61]Pargar T, Shafiee M,  Afsharkazemi MA. Designing the performance evaluation indicators of Hormozgan Social Security Organization's service supply chain by the Network Data Envelopment Analysis Model. International Journal of Finance and Managerial Accounting 2022;7(27): 105-114.
  • [62] Pendharkar PC. A hybrid genetic algorithm and DEA approach for multicriteria fixed cost allocation. Soft Computing 2017 doi: 10.10 07/s0 050 0- 017- 2605- 8.
  • [63] Ravanshad MR, Amiri A,  Salari H. Fuzzy Multi-Objective Two-Stage DEA Model for Evaluating the Performance of Companies Listed on Tehran Stock Exchange. International Journal of Finance and Managerial Accounting  2019; 3(12): 39-49.
  • [64] Seiford LM, Zhu J . Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research 2002;142(1):16–20.
  • [65] Shi X, Li Y, Emrouznejad A, Xie J, Liang L. Estimation of potential gains from bank mergers: A novel Two-stage cost efficiency DEA model. Journal of Operational Research Society 2017;68(9):1045-1055.
  • [66] Si X, Liang L, Jia G, Yang L, Wu H, Li Y. Proportional sharing and DEA in allocating the fixed cost. Applied Mathematics and Computation 2013;219(12):6580–90.
  • [67] Wang K, Huang W, Wu J, Liu YN. Efficiency measures of the Chinese commercial banking system using an additive two-stage DEA. Omega 2014;44:5–20.
  • [68] Wu J, Zhu Q, Chu J, Liu H, Liang L. Measuring energy and environmental efficiency of transportation systems in China based on a parallel DEA approach. Transportation Research Part D: Transport and Environment 2016a;48:460–72.
  • [69] Wu J, Zhu Q, Ji X, Chu J, Liang L. Two-stage network processes with shared resources and resources recovered from undesirable outputs. European Journal of Operational Research 2016b;251(1):182–97.
  • [70] Xiong B, Wu J, An Q, Chu J, Liang L. 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 2017 doi: 10.1080/03155986. 2017.1335046.
  • [71] Yu MM, Chen LH. Centralized resource allocation with emission resistance in a two-stage production system: evidence from a Taiwan’s container shipping company. Transportation Research Part A: Policy and Practice 2016;94:650–71.
  • [72] Yu MM, Chen LH, Hsiao B. A fixed cost allocation based on the two-stage network data envelopment approach. Journal of Business Research 2016;69(5):1817–22.
  • Yu Y, Shi Q. Two-stage DEA model with additional input in the second stage and part of intermediate products as final output. Expert Systems with Applications 2014;41(15):6570–4.
  • Zanella A, Camanho AS, Dias TG. Undesirable outputs and weighting schemes in composite indicators based on data envelopment analysis. European Journal of Operational Research 2015;245(2):517–30.
  • Zhang W, Wang X, Qi T, Wu X . Transmission cost allocation based on data envelopment analysis and cooperative game method. Electric Power Components and Systems 2018;46(2):208-217.
  • Zhu W, Zhang Q, Wang H. Fixed costs and shared resources allocation in two- stage network DEA. Annals of Operations  Research 2017 doi: 10.1007/s10479- 017- 2599- 8.
  • Fang L. Centralized resource allocation based on efficiency analysis for step-by-step improvement paths. Omega 2015;51:24–8.