Management Science Letters

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1 Maagemet Sciece Letters 4 (24) 2 26 Cotets lists available at GrowigSciece Maagemet Sciece Letters homepage: A applicatio of data evelopmet aalysis for measurig the relative efficiecy i bakig idustry Mehdi Soltaifar a* ad Fereshteh Farhadi b a Assistat Professor, Departmet of Applied Mathematics, Sema Brach, Islamic Azad Uiversity, Sema, Ira b M.A Studet, Departmet of Idustrial Maagemet, Sema Brach, Islamic Azad Uiversity, Sema, Ira C H R O N I C L E A B S T R A C T Article history: Received 5 Jauary 24 Received i revised format 8 March 24 Accepted March 24 Available olie 2 March 24 Keywords: Data evelopmet aalysis DEA Bakig idustry Sema Idustry Measurig the relative efficiecy of bakig idustry has bee a popular subect amog both practitioers ad academicias. Data evelopmet aalysis (DEA) has bee widely applied for differet purposes. This paper presets a empirical ivestigatio to measure the relative efficiecy of various baks located i provice of Sema, Ira. The proposed study uses DEA method to rak all uits ad usig Aderso ad Peterso method (993) [Aderse, P., & Peterse, N. C. (993). A procedure for rakig efficiet uits i data evelopmet aalysis. Maagemet Sciece, 39, ], we provide some super efficiecy for iefficiet uits. The study also provides referece umbers for iefficiet uits ad gives some target values for all iefficiet uits. 24 Growig Sciece Ltd. All rights reserved.. Itroductio Durig the past few years, there have bee tremedous efforts o applyig differet methods for measurig the relative performace of busiess uits such as activity based cost method, theory of costraits, balaced scorecard, etc. Data evelopmet aalysis (DEA) is oe of the most popular techiques amog both practitioers ad scietists (Kuah et al., 2; Cooper et al., 2). The method has bee applied for measurig techology (Khoua, 995), measurig the performace of airports (Roghaia & Foroughi, 2), supplier selectio (Levary, 28; Azar et al., 2; Nourbakhsh et al., 23) ad heath care (Ghotbuee et al., 22; Khai et al., 22). Chares et al. (978, 985, 99) are believed to be the first who itroduced the idea of measurig o-fiacial uits based o various iputs/outputs. There are various types of DEA methods icludig costat retur to scale, variable retur to scale, iput/output orieted, etc. *Correspodig author. addresses: soltaifar@khayam.ut.ac.ir (M. Soltaifar) 24 Growig Sciece Ltd. All rights reserved. doi:.5267/.msl

2 22 DEA has bee extesively implemeted i bakig idustry for may years (Camaho & Dyso, 25; Che et al., 25; Sowlati et al., 25; Edirisighe & Zhag, 27). Farkousha et al. (2) proposed a method to utilize balaced score card (BSC) as a tool for desigig performace evaluatio idices i bakig idustry. Khaki et al. (22) proposed a BSC-DEA techique to rak various decisio makig uits. They cosidered various fiacial criteria such as profit-margi, retur o assets alog with o-fiacial criteria such as customer satisfactio, advaced services, employee skills to compare the performace of differet baks. Azarbad et al. (2) preseted a BSC-DEA based model to idetify stregths, weakesses, opportuities ad threats of a firm. They cosidered there were various ucertaities associated with all iput/output parameters ad applied fuzzy umbers to hadle the ucertaities. They also cosidered a real-world case study of bakig idustry where four maor baks were possible cadidates of a partership ad implemeted the proposed model for the case study. The results have disclosed some of the issues such as weakess of electroic bakig, services ad resource allocatio as part of their ifrastructure problems. Wake ad Barros (24) measured efficiecy i Brazilia bakig usig a two-stage process where i the first stage, the umber of braches ad employees were used to attai a certai level of admiistrative ad persoel expeses per year. I the productive efficiecy stage, these expeses permitted the cosecutio of two importat et outputs icludig equity ad permaet assets. They applied the etwork-dea cetralized efficiecy model to optimize both stages, simultaeously. They reported that Brazilia baks were heterogeeous, with some cocetratig o cost efficiecy ad others o productive efficiecy. I additio, cost efficiecy was described by marketig ad admiistratio (M&A) as well as size, while productive efficiecy was described by M&A ad public status. Liu et al. (29) applied DEA techique to measure the relative efficiecies o a bak i Taiwa ad studied the performace ad productivity chages whe baks implemet fiacial electroic data iterchage. They icluded 8 braches of the performace for implemetatio of fiacial electroic data iterchage of the overall efficiecy, pure techical efficiecy, scale efficiecy, aalysis of referece groups ad the potetial to improve the value of aalysis for differet brach performace assessmets. The empirical results show that case bak could adopt the DEA evaluatio model as refereces to upgrade the overall operatig performace effectively for creatig competitive advatages. Wag et al. (24) utilized etwork DEA method to evaluate efficiecies of the Chiese commercial baks. 2. The proposed study I this paper, we preset a output orieted data evelopmet aalysis to measure the relative efficiecy of a Iraia private bak amed Bak Mehr located i provice of Sema, Ira. The study also uses Aderse ad Peterse (993) for supper efficiecy measuremet ad provides some additioal iformatio for rakig efficiet baks. 2.. The DEA method The costat retur to scale DEA (CCR) was first itroduced by Chares, et al. (978, 994) for measurig the relative efficiecy of decisio makig uits (DMU). This method allows us to uderstad how a give DMU works wheever a productio fuctio is available. However, i may cases obtaiig a aalytical form for this fuctio is ot available. Therefore, we may form a set of productio feasibility, which costituts of various priciples such as fixed-scale efficiecy, covexity ad feasibility as follows, T C ( X, Y) X X, Y Y,,,, ()

3 M. Soltaifar ad F. Farhadi / Maagemet Sciece Letters 4 (24) 23 where X ad Y state the iput ad output vectors, respectively. The CCR productio feasibility set border presets the relative efficiecy where ay off-border DMU is stated as iefficiet. The CCR model ca be computed i two kids of either iput or output orieted. The iput CCR aims to decrease the maximum iput level with a ratio of so that, at least, the same output is produced, i.e.: mi subect to X X p Y r Y rp, i,,,,. Model (2) is a evelopmet form of iput CCR where is the relative efficiecy of the DMU ad it is possible to show that the optimal value of, *, is located betwee zero ad oe. I a iput orieted DEA model, oce the efficiecy of a DMU uit, DMU p, lies i case of iefficiecy, oe may directs it towards the border to chage it efficiet. I the case of the output orieted DEA model, the primary obective is to maximize the output level,, by usig the same amout of iput. The model ca be formulated as follows, (2) mi subect to X i X Y Y ip ip,,,.,, (3) There are literally various types of DEA method ad the BCC output orieted DEA model is used i this paper, which is as follows, s m max z Sr Si r i subect to r r r,,,,, y S y r s r r r x S x i,, m, si, sr, free i sig The results of the DEA implemetatio ormally lead us to have more tha oe efficiet uit ad it is possible to use the method developed by Aderse ad Peterse (993) to rak efficiet uits, separately. I order to covert the iefficiet uits to efficiet oes, we eed to use phase III of this method, which gives better image of the whole system as follows,

4 24 mi W subect to x x x, i,..., m, R R R i i io io y y y, r,..., s, * r r ro ro, p, i,..., m, q, r,..., s, p W, q W, i r,,...,. where i ad i associated with dual variable ad both are limited withi bouds i p ad r q. The problem uses the followig method for covertig iefficiet uit ito efficiet oes. xˆ x, i,..., m, io io i * ˆ ro ro r,,...,, y y r s The proposed study of this paper has four levels. I the first level, the study determies the iput/output parameters. I the secod stage, BCC method is applied to rak all baks, ad the efficiet uits are raked i the third stage usig Aderso ad Peterso method. Fially, i fourth stage, we use model (4) to brig iefficiet method close to efficiet frotier. Table shows iput/output of the proposed study. Table The summary of iput/output Iput Output Brach Equipmet Employee Profit Resources absorbed As we ca observe from the results of Table, the proposed study cosiders two iputs, equipmet ad employee, ad two outputs, profit ad resources absorbed, for 2 differet baks located i provice of Sema, Ira. 3. The results I this sectio, we preset details of our implemetatio of DEA method for 2 braches of bak. Table 2 shows details of our proposed model. Table 2 The summary of BSC method Brach Efficiecy Dual variable (4) (5)

5 M. Soltaifar ad F. Farhadi / Maagemet Sciece Letters 4 (24) 25 As we ca observe from the results of Table 2, there are six uits, which are efficiet ad the remaiig six uits are cosidered as iefficiet uits. The implemetatio of Aderso ad Peterso are summarized i Table 3 as follows, Table 3 The result of the implemetatio of supper efficiecy usig Aderso & Peterso techique Uit umber Rak Next, we have to fid a idex to covert the iefficiet uits ito a efficiet oe. Table 4 shows details of our fidigs. Table 4 The summary of referece uits alog with their weights Uit Accordig to Table 4, uit ca become efficiet through two uits of 3 ad 7 ad the secod bak ca also become efficiet through uit 3 ad 2. Based o the iformatio, we may provide efficiet amout of resources ad Table 5 shows details of our fidigs. Table 5 The summary of efficiet amout of iputs/outputs Iput Output Brach Equipmet Employee Profit Resources absorbed Coclusio This paper has preseted a empirical ivestigatio to measure the relative efficiecy of various baks located i provice of Sema, Ira. The proposed study has applied DEA method to rak all uits ad usig Aderso ad Peterso method, we have provided some super efficiecy for iefficiet uits. We have also provided referece umbers for iefficiet uits ad provided target values for all iefficiet uits. Refereces Aderse, P., & Peterse, N. C. (993). A procedure for rakig efficiet uits i data evelopmet aalysis. Maagemet Sciece, 39,

6 26 Azarbad, M., Ekhtiari, M., Sarfaraza, A & Abdi, F. (2). A framework to select commercial bak parter usig fuzzy BSC-DEA method. Maagemet Sciece Letters, (4), Azar, A., Olfat, L., Khosravai, F., & Jalali, R. (2). A BSC method for supplier selectio strategy usig TOPSIS ad VIKOR: A case study of part maker idustry. Maagemet Sciece Letters, (4), Camaho, A. S., & Dyso, R. G. (25). Cost efficiecy measuremet with price ucertaity: a DEA applicatio to bak brach assessmets. Europea Joural of Operatioal Research, 6(2), Chares, A., Cooper, W.W., & Rhodes, E. (978). Measurig the efficiecy of decisio makig uits. Europea Joural of Operatioal Research, 2(6), Chares, A., Cooper, W.W., Golay, B., Seiford, L.M., & Stutz, J. (985). Foudatios of data evelopmet aalysis ad Pareto-Koopmas empirical productio fuctios. Joural of Ecoometrics, 3(-2), 9-7. Chares, A., Cooper, W.W., Huag, Z.M., & Su, D.B. (99). Polyhedral coe-ratio DEA models with a illustrative applicatio to large commercial baks. Joural of Ecoometrics, 46(-2), Che, X., Skully, M., & Brow, K. (25). Bakig efficiecy i Chia: Applicatio of DEA to pre-ad post-deregulatio eras: Chia Ecoomic Review, 6(3), Cooper, W.W., Lawrece, M.S., & Zhu, J. (2). Hadbook o data evelopmet aalysis. Iteratioal Series i Operatios Research & Maagemet Sciece, Spriger, 64, -4. Edirisighe, N. C. P., & Zhag, X. (27). Geeralized DEA model of fudametal aalysis ad its applicatio to portfolio optimizatio. Joural of Bakig & Fiace, 3(), Farkousha, S., Naafi, E & Aryaezhad, M. (2). A BSC-DEA approach to measure the relative efficiecy of service idustry: A case study of bakig sector. Iteratioal Joural of Idustrial Egieerig Computatios, 2(2), Ghotbuee, A., Hemati, M & Fatemiezhad, R. (22). A empirical study based o BSC-DEA to measure the relative efficiecies of differet health care ceters i provice of Sema, Ira. Maagemet Sciece Letters, 2(7), Khaki, A., Naafi, S & Rashidi, S. (22). Improvig efficiecy of decisio makig uits through BSC- DEA techique. Maagemet Sciece Letters, 2(), Khai, F., Naderi, H., Zageeh, M., & Fazeli, E. (22). Measurig the relative efficiecy of Ilam hospitals usig data evelopmet aalysis. Maagemet Sciece Letters, 2(4), Khoua, M. (995). The use of data evelopmet aalysis for techology selectio. Computers ad Idustrial Egieerig, 28(), Kuah, C.T., Wog, K.Y., & Behrouzi, F. (2). A review o data evelopmet aalysis (DEA). Proc. of 4 th Asia Iteratioal Coferece o Mathematical/Aalytical Modellig ad Computer Simulatio, Levary, R.R. (28). Usig the aalytic hierarchy process to rak foreig suppliers based o supply risks. Computers ad Idustrial Egieerig, 55(2), Liu, Z., Li, F., & Fag, L. P. (29). A study of applyig DEA to measure performace o bak implemetig fiacial electroic data iterchage. Iteratioal Joural of Electroic Busiess Maagemet, 7(4), Nourbakhsh, V., Ahmadi, A & Mahootchi, M. (23). Cosiderig supply risk for supplier selectio usig a itegrated framework of data evelopmet aalysis ad eural etworks. Iteratioal Joural of Idustrial Egieerig Computatios, 4(2), Roghaia, E., & Foroughi, A. (2). A empirical study of Iraia regioal airports usig robust data evelopmet aalysis. Iteratioal Joural of Idustrial Egieerig Computatios, (), Sowlati, T., Paradi, J. C., & Suld, C. (25). Iformatio systems proect prioritizatio usig data evelopmet aalysis. Mathematical ad Computer Modellig, 4(), Wake, P., & Barros, C. (24). Two-stage DEA: A applicatio to maor Brazilia baks. Expert Systems with Applicatios, 4(5), Wag, K., Huag, W., Wu, J., & Liu, Y. N. (24). Efficiecy measures of the Chiese commercial bakig system usig a additive two-stage DEA. Omega, 44, 5-2.

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