Management Science Letters

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1 Maagemet Sciece Letters 3 (203) Cotets lists available at GrowigSciece Maagemet Sciece Letters homepage: A DEA applicatio for aalyzig ivestmet activities i higher educatioal orgaizatios Zahra Azizi a* ad Mehdi Paktiat b a Departmet of Accoutig, Sciece ad Research Brach, Islamic Azad Uiversity, Saveh, Ira b 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 October 2, 202 Received i revised format 29 November 202 Accepted 28 December 202 Available olie Jauary Keywords: DEA Efficiecy Uiversity Private schools play importat role o developig ecoomy especially i rural areas of Ira ad whe they operate efficietly it ca also be cosidered as a rich source of icome. Durig the past three decades, data evelopmet aalysis (DEA) has become a popular techique for measurig the relative performace of o-fiacial uits. I this paper, we preset a empirical study to measure the relative efficiecy of private uiversities located i regio te of Islamic Azad uiversity. The proposed study of this paper assigs some poits for huma resources icludig uiversity professor ad regular employees ad cosiders it alog with assets as iputs of DEA model. We also cosider the umber of graduated studets ad operatig profit as output of our proposed DEA model. The implemetatio of stadard BCC method yields 6 efficiet uits ad to have better results we use aother DEA techique. The results of this study preset some ivestmet opportuities for maagemet of this private uiversity. 203 Growig Sciece Ltd. All rights reserved.. Itroductio Private schools play importat role o developig ecoomy especially i rural areas of Ira ad whe they operate efficietly it ca also be cosidered as a rich source of icome. Durig the past three decades, data evelopmet aalysis (DEA) (Chares et al., 978, 994; Aderse et al., 993) has become a popular techique for measurig the relative performace of o-fiacial uits. Fallah et al. (20) used DEA aalysis o bakig sector by cosiderig various fiacial ad o-fiacial iputs ad outputs ad measured the relative efficiecies of various braches of baks ad aalyzed them uder differet scearios. Avkira (200) studied the relatioship betwee the supper-efficiecy estimatios ad some maor importat fiacial ratios for some Chiese bakig sector. The survey provided foud the iefficiet uits where there was a low correlatio betwee the supper-efficiecy ad desirable fiacial ratios. Staub et al. (200) studied differet factors affectig the relative efficiecy of Brazilia baks icludig cost ad techical efficiecies over the period *Correspodig author. addresses: daaei@yahoo.com (Z. Azizi) 203 Growig Sciece Ltd. All rights reserved. doi: /.msl

2 436 Li et al. (2009) used differet DEA methods for 7 braches of a certai bak i Taiwa ad reported a overall techical efficiecy of 54.8% amog them. Yag et al. (200) studied bak performace ad maagemet plaig based o hybrid miimax referece poit DEA approach. Zaheri et al. (202) ivestigated customer loyalty ad prioritizig based oe private bak i Kurdista provice. I this paper, we preset a empirical study to measure the relative efficiecy of private uiversities located i regio te of Islamic Azad uiversity. The orgaizatio of the paper first presets details of the propsoed method i sectio 2. The results are discussed i sectio 3 ad cocludig remarks are give i the last to summarize the cotributio of the paper. 2. The proposed study The proposed study of this paper uses DEA as a primary tool for measurig the relative performace of all Islamic Azad uiversity, which are active i regio te ad the primary obective is to look for ivestmet activities accomplished durig the fiscal year of 20. Fig. demostrates the structure of the proposed study of this paper. Uiversity th uit (Idepedet variable) Year of activity (Cotrol variable) Iputs (Idepedet variable) (Employee poits, Uiversity assets) Outputs (Idepedet variable) (Operatig profit, Graduate studets) Uiversity th uit efficiecy (Depedet variable) Fig.. The framework of the proposed study The proposed study is cosidered as a applied research ad the purpose of the research is to measure the relative performace of the biggest uiversity uits i regio 0 i terms of ivestmet activities. Fig. 2 demostrates details of our proposed study. Start Determie the efficiet uits Extracts ivestmet attributes Data gatherig Build DEA Measure efficiecy Use Cook & Kress method No Coclusio ad suggestios Rakig complete? Yes Ed Fig. 2. The procedure of the proposed study

3 Z. Azizi ad Mehdi Paktiat / Maagemet Sciece Letters 3 (203) 437 I our study, we ivestigate whether we could improve the relative efficiecy of a particular uit through mergig the uit with aother uit. We also perform a ivestigatio to detect the best model for measurig the relative efficiecy. Chares, et al. (978, 994) are believed to be the first who itroduced the idea of costat retur to scale DEA (CCR) as a mathematical techique for measurig the relative efficiecy of decisio makig uits (DMU). It is a easy task to show that DMU works wheever a productio fuctio is available. However, i differet cases obtaiig a aalytical form for this fuctio is ot practical. Therefore, we form a set of productio feasibility, which icludes some priciples such as fixed-scale efficiecy, covexity ad feasibility as follows, T C = ( X, Y ) X λ X, Y λ Y, λ 0, =, L, () where X ad Y are iput ad output vectors, respectively. The CCR productio feasibility set border defies the relative efficiecy i which ay off-border DMU is cosidered as iefficiet poit. The CCR model is determied i two forms of either iput or output orieted. The iput CCR aims to decrease the maximum iput level with a ratio of θ so that, at least, the same output is produced, i.e.: mi θ subect to θ X λ X p λ Y r Y λ =, rp, i 0, λ 0, =, L,. (2) Model (2) is called DEA form of iput CCR where θ is the relative efficiecy of the DMU ad we ca verify that the optimal value of θ, θ *, is a umber betwee zero ad oe. We may write the dual of model (2) as follows, mi s r= uy r subect to m i= m vx i i0 + u r0 0 =, vx vx + u 0,,,. i i0 ip i i 0 i= i= m L u 0, r =, L, s. r v 0, i =, L, m i (3) I case we cosider the dual fuzzy two-phase BCC form, the first phase is as follows,

4 438 max : φ subect to μ φ free. μ x x, i =,..., m i i0 μ y φy, r =,..., s r r0 μ =, =,..., 0, =,..., (3) I additio, the secod phase of fuzzy BCC is as follows, max : subect to m s + w= S + S i i= r= i i i0 + r r r0 r μ x + S = x, i =,..., m μ y S = φ y, r =,..., s μ =, =,..., + μ 0, =,..., S 0, i =,..., m S 0, r =,..., s. i r Oe of the issues associated with DEA method arises whe some of the dual variables appear to be zero i optimality. I such a case, there are more tha oe iefficiet uit ad two uits havig the same output ad differet iputs could both be cosidered iefficiet with the ratios. This is ot a correct observatio sice oe uit is more efficiet that the other oe. I such a case we may use a approach developed by Cook ad Kress (990). The model presets the best model for collectio ballot votig results ad for each cadidate, it provides a fair assessmet for the first, the secod ad other cadidates. Let y r be the total umber of votes for cadidate th ad ɛ be a small umber as a lower boud for decisio makig uit. For the sake of simplicity we cosider d(r, ɛ)= ɛ. Therefore we have, subect to, =,,, 0, 0

5 Z. Azizi ad Mehdi Paktiat / Maagemet Sciece Letters 3 (203) The results I this sectio, we preset the results of the implemetatio of our proposed study. The proposed study of this paper assigs some poits for huma resources icludig uiversity professor ad regular employees ad cosiders it alog with assets as iputs of DEA model. Table demostrates iputs/outputs of the proposed model. Table Iputs/outputs of the proposed model Iputs Uit Assets Huma resource poits Azad shahr () 7, Badar Gaz (2) 60, Damgha (3) 9, Sema (4) 94, Shahrood (5) 23, Aliabad (6) 62, Gorga (7) 98, Garmsar (8) 45, Mahdishahr (9) 8, Gobad Kaboos (0) 2, Mioodasht() 2, Outputs Graduated studets Operatig profit Applyig DEA method usig BCC techique helps determie relative efficiecies of the proposed model summarized i Table 2 as follows. Table 2 The results of relative efficiecy Uit Efficiecy Eff./Ieff Rak We have calculated how we ca improve the relative efficiecy of iefficiet uits to become efficiet ad the results are summarized i Table 3. Table 3 The results of ecessary improvemet required to covert iefficiet uits to efficiet oes Preset output Ideal output Uit Graduated Operatig Operatig profit Graduated studets(gap) studets profit(gap) Azad shahr () Badar Gaz (2) Damgha (3) (4%) 57.58(68%) Sema (4) Shahrood (5) Aliabad (6) (40%) (72%) Gorga (7) (04%) (90) Garmsar (8) (43%) (86) Mahdishahr (9) Gobad Kaboos (0) (22) (52) Mioodasht()

6 440 Table 3 shows the amout of additioal output each iefficiet uit eeds to add to become efficiet oe. The results also demostrate the relative gap betwee actual ad desirable outputs. I additio, as we ca observe from the results of Table 3, six out of eleve uits have become efficiet. Therefore, we eed to use Cook ad Kress (990) method to rak efficiet uits ad we first report cross DEA for measurig relative efficiecy of various uits based o BCC method ad Table 4 summarizes the results. I additio, Table 5 shows details of rakig based o the results of Table 4. Table 4 The summary of relative efficiecy usig Cross DEA usig BCC techique Uit () (2) (3) (4) (5) (6) (7) (8) (9) (0) () () (2) (3) (4) (5) (6) (7) (8) (9) (0) () Table 4 The summary of raks of various uits usig Cross DEA usig BCC techique Uit () (2) (3) (4) (5) (6) (7) (8) (9) (0) () () (2) (3) (4) 2 2 (5) (6) (7) (8) (9) (0) () 2 Fially, we summarize the frequecies of six efficiet uits compared with eleve uits ad Table 5 demostrates the results of our survey. Table 5 The frequecy of raks i differet cities Uit Azad Shahr Badar Gaz Sema Shahrood Mehdi Shahr Miodasht Now we ca use Cook ad Kress (990) techique to fid the relative rakig ad Table 6 summarizes the results of our survey.

7 Z. Azizi ad Mehdi Paktiat / Maagemet Sciece Letters 3 (203) 44 Table 6 The results of the BCC ad Cook & Kross techiques ad fial rakig BCC Cook ad Kress Uit Efficiecy Rak Efficiecy Azad shahr () Badar Gaz (2) Damgha (3) Sema (4) Shahrood (5) Aliabad (6) Gorga (7) Garmsar (8) Mahdishahr (9) Gobad Kaboos (0) 0.5 Mioodasht() Rak Fial rak As we ca observe from the results of Table 6, two cities, Azad shahr ad Badar Gaz, are the best cadidate for ivestmet followed by Sema, Mioodasht, Mahdishahr. 4. Coclusio I this paper, we have preseted a empirical ivestigatio to measure the relative efficiecy of private uiversities located i regio te of Islamic Azad uiversity. The proposed study of this paper assiged some poits for huma resources icludig uiversity professor ad regular employees ad cosidered it alog with assets as iputs of DEA model. We have also cosidered the umber of graduated studets ad operatig profit as output of our proposed DEA model. The implemetatio of stadard BCC method yielded 6 efficiet uits ad to have better results we have used aother DEA techique. The results of this study preseted some ivestmet opportuities for maagemet of this private uiversity. Ackowledgmet The authors would like to thak the officials of Islamic Azad uiversity for providig ecessary iformatio ad supportig this proect. Refereces Avkira, N. K. (200). Associatio of DEA super-efficiecy estimates with fiacial ratios: Ivestigatig the case for Chiese baks. Omega, 39(3), Aderso, P., & Peterso, N. C. (993). A procedure for rakig efficiet uits i data evelopmet aalysis. Maagemet Sciece, 39(0), Cook, W. D., & Kress, M. (990). A data evelopmet model for aggregatig preferece rakigs. Maagemet Sciece, 36, Chares A, Cooper, W. W., Rhodes, E. (978). Measurig the efficiecy of decisio makig uits. Europea Joural of the Operatioal Research, 2, Chares A, Cooper W. W., Lewi, A., Seiford, L. M. (994). Data evelopmet aalysis: theory, methodology ad applicatios. Massachusetts: Kluwer Academic Publishers. Che, S. J., & Hwag, C. L. (992). Fuzzy multiple attribute decisio makig: Methods ad applicatios. Berli: Spriger-Verlag. Fallah, M., Aryaezhadb, M.B., Naafi, S.E., & Shahsavaripour, N. (20). A empirical study o measurig the relative efficiecy usig DEA method: A case study of bak idustry. Maagemet Sciece Letters, (),

8 442 Li, T. T., Lee, Ch-Ch., & Chiu, T-F. (2009). Applicatio of DEA i aalyzig a bak's operatig performace. Expert Systems with Applicatios, 36(5), Saaty, T. L. (992). How to make a decisio: the aalytic hierarchy process. Europea Joural of Operatioal Research, 48, Staub, R. B., Da Silva e Souza, G. & Tabak, B. M. (200). Evolutio of bak efficiecy i Brazil: A DEA approach. Europea Joural of Operatioal Research, 202(), Yag, J.B., Wog, B.Y.H., Xu, D.L., Liu, X.B. & Steuer, R.E. (200). Itegrated bak performace assessmet ad maagemet plaig usig hybrid miimax referece poit DEA approach. Europea Joural of Operatioal Research, 207(3), Zaheri, F., Farughi, H., Soltapaah, H., Alaiazar, S., & Naseri, F. (202). Usig multiple criteria decisio makig models for rakig customers of bak etwork based o loyalty properties i weighted RFM model. Maagemet Sciece Letters, 2(),