Maagemet Sciece Letters 3 (203) 435 442 Cotets lists available at GrowigSciece Maagemet Sciece Letters homepage: www.growigsciece.com/msl 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 4 203 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 2000-2007. *Correspodig author. E-mail addresses: daaei@yahoo.com (Z. Azizi) 203 Growig Sciece Ltd. All rights reserved. doi: 0.5267/.msl.203.0.004
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
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,
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
Z. Azizi ad Mehdi Paktiat / Maagemet Sciece Letters 3 (203) 439 3. 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 () 7,689.03 800 Badar Gaz (2) 60,203.25 2429 Damgha (3) 9,07.46 0658 Sema (4) 94,87.98 5228 Shahrood (5) 23,795.47 24676 Aliabad (6) 62,375.92 3333 Gorga (7) 98,3.66 886 Garmsar (8) 45,483.24 895 Mahdishahr (9) 8,983.98 2953 Gobad Kaboos (0) 2,44.07 3262 Mioodasht() 2,594.30 2220 Outputs Graduated studets 23 300 984 860 763 43 407 460 00 85 23 Operatig profit 25386-4895 - 406-3093 - 436-3490 - 34937-4359 - 2795-7478 - 4252 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 2 3 4 5 6 7 8 9 0 Efficiecy 0.68 0.68 0.90 0.83 0.50 Eff./Ieff. - - - - - Rak 9 9 7 8 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 () 23 25386 Badar Gaz (2) 300-4895 Damgha (3) 984-406 457(4%) 57.58(68%) Sema (4) 860-3093 Shahrood (5) 763-436 Aliabad (6) 43-3490 586(40%) 586.46(72%) Gorga (7) 407-34937 565(04%) 462.53(90) Garmsar (8) 460-4359 699(43%) 0976.8(86) Mahdishahr (9) 00-2795 Gobad Kaboos (0) 85-7478 359(22) 676.28(52) Mioodasht() 23-4252
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) () () 00-74.788 55.35 33.952 60.406 68.92 43.373 - - - (2) 30.335 00 2.852 8.279.077 8.087 2.44 3.593 63.333 58.686 86.885 (3) 8.529-67.56 45.526 27.889 49.85 56.334 35.479 - - - (4) - - - 00 6.256 - - 77.002 - - - (5) - - - - 00 - - - - - - (6) 93.49-69.786 5.85 3.792 67.56 64.437 40.56 - - - (7) - - 84.526 68.235 4.64 69.97 90.09 5.557 - - - (8) - - 9.475 73.42 44.648 74.742 87.72 82.64 - - - (9) - - - - - - - - 00 - - (0) 36.462 64.93 24.295 25.424 5.57 2.08 26.995 7.349 45.726 49.5 67.854 () - 83.334 - - - - - - - - 00 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) () () 3 4 5 4 3 4 (2) 5 7 8 9 7 7 8 2 2 (3) 3 5 6 7 5 5 6 (4) 2 2 (5) (6) 2 4 5 6 3 4 5 (7) 2 3 4 2 3 (8) 2 3 2 (9) (0) 4 3 6 7 8 6 6 7 3 2 3 () 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 2 3 4 5 6 7 8 9 0 Azad Shahr 0 2 3 0 0 0 0 0 0 Badar Gaz 2 2 0 0 0 3 2 0 0 Sema 2 0 0 0 0 0 0 0 0 0 Shahrood 0 0 0 0 0 0 0 0 0 0 Mehdi Shahr 0 0 0 0 0 0 0 0 0 0 Miodasht 0 0 0 0 0 0 0 0 0 Now we ca use Cook ad Kress (990) techique to fid the relative rakig ad Table 6 summarizes the results of our survey.
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) 0.68 9 Sema (4) 0.749 Shahrood (5) 0.4987 Aliabad (6) 0.68 9 Gorga (7) 0.9 7 Garmsar (8) 0.83 8 Mahdishahr (9) 0.4987 Gobad Kaboos (0) 0.5 Mioodasht() 0.4994 Rak 3 5 5 4 Fial rak 9 3 5 9 7 8 5 4 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), 323 334. Aderso, P., & Peterso, N. C. (993). A procedure for rakig efficiet uits i data evelopmet aalysis. Maagemet Sciece, 39(0), 26-264. Cook, W. D., & Kress, M. (990). A data evelopmet model for aggregatig preferece rakigs. Maagemet Sciece, 36, 302 30. Chares A, Cooper, W. W., Rhodes, E. (978). Measurig the efficiecy of decisio makig uits. Europea Joural of the Operatioal Research, 2, 429 44. 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, (), 49-56.
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