AN AHP(ANALYTIC HIERARCHY PROCESS)-BASED INVESTMENT STRATEGY FOR CHARITABLE ORGANIZATIONS OF GOODGRANT FOUNDATION

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1 Iteratioal Joural of Maagig Iformatio Techology (IJMIT) Vol.9, No.2, May 207 AN AHP(ANALYTIC HIERARCHY PROCESS)-BASED INVESTMENT STRATEGY FOR CHARITABLE ORGANIZATIONS OF GOODGRANT FOUNDATION ABSTRACT Xue-yig Liu, Jia-sheg Yag, Xiao-ya Fei ad Ze-ju Tao College of Sciece, Shaghai Uiversity, Shaghai, , Chia This paper provides the optimal ivestmet strategy for the Goodgrat Foudatio. To determie the schools to be ivested, firstly we fid the factors about improvig studets educatioal performace, icludig urgecy of studet s eeds, school s demostrate potetial for effective use of private fudig, the reputatio of school, ad retur o ivestmet etc; secodly, we utilize AHP (Aalytic Hierarchy Process) to determie the weight of every factor ad rak the schools i the list of cadidate schools accordig to the composite idex of every school calculated from the weight. To cofirm the ivestmet per school ad obtais the ivestmet duratio time, we use DEA (Data Evelope Aalyse) to get chages of scale efficiecy; ad the accordig to the chage tred, we determie time duratio of ivestmet ad effective utilizatio of private fudig, which is the factor together with studet populatio affectig the ivestmet amout for per school. It is helpful to make a better decisio o ivestig uiversities, We are coviced that our research is promisig to beefit all sides of studets, schools ad Goodgrat. KEYWORDS AHP, DEA, Educatioal Performace, Ivestmet Strategy. INTRODUCTION Uiversities ad colleges are places where youg studets gai valuable kowledge, resources ad opportuities before they step ito the society. That is why may foudatios are willig to ivest o udergraduates to help improve their educatioal performace. With so may uiversities ad colleges i America, it is ecessary for us to carry out a method about how to determie a optimal ivestmet strategy to idetify the schools, the ivestmet amout per school efficietly ad objectively. How to distribute the fud is exactly the key. It is a multiaspect evaluate task icludig the urgecy of studets eeds, school s demostrate potetial for effective use of private fudig, the reputatio of school, retur o ivestmet etc. Mea while, the time duratio that the orgaizatio s moey have the highest likelihood of producig a strog positive effect o studet performace should also be a primary cosideratio. OtherlargeadkowgratorgaizatiossuchasGatesFoudatioadLumiaFoudatio show the curret way to ivestigate the quailficatio which maily cocetrates o the low icome of studets families ad potetial of uiversities. These models will take the ability of usig the fudig ad rate of retur ito accout, ad obtai approximate ivestmet duratio time ad retur of ivestmets oth at the Good grat Foudatio ca provide the assistace best to ot oly studets but also schools ad foudatio itself. The aalytic hierarchy process (AHP)[2-4] is a structured techique for orgaizig ad aalyzig complex situatio. It is based o mathematics ad psychology. Rather tha prescribe a correct decisio, the AHP helps decisio makers fid oe that best suits their goal ad their uderstadig of the problem[5-6]. It provides a comprehesive ad ratioal framework for DOI : 0.52/ijmit

2 Iteratioal Joural of Maagig Iformatio Techology (IJMIT) Vol.9, No.2, May 207 structurig a decisio problem, for represetig ad quatifyig its elemets, for relatig those elemets to overall goals, ad for evaluatig alterative solutios. This paper provides the optimal ivestmet strategy for the Goodgrat Foudatio by AHP method[2]. It helps improv educatioal performace of udergraduates i Uited States ad make them graduate successfully, live a good life i the future. The rest of this paper is orgaized as follows: i Sectio 2, wepresetourmodel approach i detail, icludig the aalytical hierarchy process model addata evelope aalysemodel.coclusios are provided i the last Sectio. 2. MODEL DESIGN 2. THE ANALYTICAL HIERARCHY PROCESS MODEL By usig cluster aalysis, We group all the colleges corecard data ito urgecy of studets eeds, school s demostrate potetial for effective use of private fudig, the reputatio of school, retur o ivestmet 4 groups. Meawhile urgecy of studets eeds cotais share of part-time udergraduates, media debt of completers ad average et price; School s demostrate potetial for effective use of private fudig cotais percetage of udergraduates who have received a PellGrat, percet of all federal uder graduate studets receivig a federal studet loa ad 3- year repaymet rate; The reputatio of school icludes predomiat degree awarded, disciplie distributio ad structure ad whether it is operatig with other istitutios; Retur o ivestmet icludes Media earigs of studets 0 years after etry, share of studets earig over 25,000dollar/year 6 years after etry. The dates of 2936 uiversities are i Table. Table : Dates of 2936 Uiversities 2.. THE ESTABLISHMENT OF A HIERARCHY The problem of the case ca be divided ito three layers i order. 28

3 Iteratioal Joural of Maagig Iformatio Techology (IJMIT) Vol.9, No.2, May THE WEIGHTS OF LAYER C IN LAYER O Cosiderig the relative importace of C compared with C 2, C 3, C 4 ; we might arrive at the followig pair wise compariso matrix A The maximum eigevalue λ = 4.05, ad we ca get the correspodig ormalized eigevector w = (0.58,0.7,0.6,0.09) CONSISTENCY TEST Cosistecy Idex CI max whe = 4,λ = 4.05,CI = 0.06, Radom Cosistecy Idex RI = 0.9,it ca be get from the table below(table 2). Table 2: Radom Cosistecy Idex Cosistecy Ratios CI CR RI Whe RI = 0.9, CR = 0.08 < 0. meet the ispectio. 29

4 Iteratioal Joural of Maagig Iformatio Techology (IJMIT) Vol.9, No.2, May THE WEIGHTS OF LAYER P IN LAYER C Cosiderig the relative importace of P compared with P 2,P 3 ;P 4 compared with P 5,P 6 ;P 7 compared with P 8,P 9 ;P 0 compared with P ; We might arrive at the followig pairwise compariso matrix: B B B B The maximum eige value λ 2 = 3,λ 3 = 3,λ 4 = 3.0,λ 5 = 2 ad we ca get the correspodig ormalized eige vector w = (0.2,0.6,0.2) T w 2 = (0.2,0.2,0.6) T w 3 = (0.635,0.287,0.078) T w 4 = (0.3,0.7) T After ormalizatio, we ca weight vector CR 4 () K 2 CR 2 i 2..5 THE WEIGHTS OF LAYER P IN LAYER O W (,....,)(,2,3,4) k ()()()() k k k k 2 W [ W, W, W, W ] ( )( 2)( 3)( 4) 2 4 ()( 2)(3)( 4) WW W[ W, W, W, W ]( W0. 5,0. 345,0. 5,0. 035,0. 035,0. 0 6,0. 099,0. 045,0. 02,0. 03,0. 065) 2 CR CR CR DATA NORMALIZATION METHOD I order to recocile all kids of idicator si oe assessmet system, we apply Mi Max Normalizatio to ormalize the idicators that metioed i the database. This helps us to process data i various dimesio. Our process of data ormalizatio is as followig formula x x * mi max mi s

5 Iteratioal Joural of Maagig Iformatio Techology (IJMIT) Vol.9, No.2, May COMPREHENSIVE RANK We ca figure out the followig formula to quatize the satisfactio of Goodgrat to the school. D i i j j j b W( i,,2936) Lastly, we utilize Aalytic Hierarchy Process (AHP) to determie the weight of everyfactoradraktheschoolsithelistofcadidateschoolsaccordigtothecomposite idex of every school calculated from the weight. Tha we ca select schools i the top of the rak to ivest suitable fuds. 3

6 Iteratioal Joural of Maagig Iformatio Techology (IJMIT) Vol.9, No.2, May DATA ENVELOPE ANALYSE 2.2. BASIC CONCEPTION OF DEA After assessig the educatioal performace of all post secodary colleges ad uiversities,i accordace with the rak,we select 200 uiversities who are most deservig grats. The it comes to the questio of the amout of moey distributed to per school. We cosider the ability of effective usig of private fudig ad the populatio as the mai factors. To quatize the fudig use capacity, we evaluate the relative efficiecy of the same type of output ad iput Decisio Makig Uit(DMU) ad employ the Date Evelopmet Aalysis (DEA)[8-9]. Parameter Assumptio :X: iput idex,y : output idex, to a certai project we assume that there are s decisio makig uits per uit of which has m kids of iputs ad kids of iputs, weight coefficiet correspodigly V=(v,v 2,v 3,,v m ) T,U=(u,u 2,u 3,,u m ) T,every uit hasits ow efficiecy evaluatio goals(h), h j = uy j /vx j,we ca always choose proper weight coefficiet which satisfy h j,j =,2,,s. I order to estimate the efficiecy of DMU, weight coefficiet correspodigly v,u as variable, aim at the efficiecy idex of DMU,restrait by all efficiecy idexes,develop the fractioal programmig model as followed: Max h k u y r r m v x i i r k i k r r k r.. m st u y v x i i I which i k ur 0 0 v i LetU t u V t v U 0V 0 after Chares-Cooper trasform we get C 2 R r r i i r i liear programmig model Max h U y k r t k r m v x i i k i st.. U y m v x r r j i i j r i 0 Itroduceslackvariables-adsurplusvariables+adgettheCCRDualityliearlayout model Max [() ] e s e s st.. x s x r j j j 0 32

7 Iteratioal Joural of Maagig Iformatio Techology (IJMIT) Vol.9, No.2, May 207 j y s y j j j 0 I which: θ k presets the potetial quota of all iputs possibility of equal proportio reductio. e ΛT,e T preset m dimesio uit colum vector ad dimesio uit colum vector. ε presets The Archimedes dimesioless, which is smaller tha ay umber bigger tha zero THE SOURCE OF SAMPLE DATA After disposal data we choose the amout of Pell Grat ad federal studet loa as iput idexes, the amout of earigs of studets workig ad ot erolled 0 years after etry ad high i come studets 6years after etry as output idexes. The processed data was showed i the followig table(fig4) ESTABLISHMENT OF MODEL CCR Model Max h U y U y u u u u v v u u v v u u v v u u v v u u v v u u v v u, u, v, v

8 BCC model Mi Iteratioal Joural of Maagig Iformatio Techology (IJMIT) Vol.9, No.2, May s s s s ,,,, s, s CALCULATING We adopt calculatig software Deap Versio 2. developed by professor Coelli to process the sample data o the table ad get the efficiecy of DMU(θ) ad slack variable(s,s +). Figure 5: computatioal results of Deap Versio 34

9 Iteratioal Joural of Maagig Iformatio Techology (IJMIT) Vol.9, No.2, May APPLICATION To balace the amout of moey for per school. Whether the school ca maximize the value of fudig it receives is the major cosideratio factor plus the populatio effect. We divide the two factors as 7:3, ad makig the fial decisio accordig to each weightig. Part of the table has bee showed o the below(fig.6) FURTHER THINK To decide the duratio that the orgaizatio s moey should be provided, the mai aspect we cosider is to stimulate the highest likelihood of producig a strog effect o studet performace. So we cosider the chage coditio of the retur to scale i DMU: If 0 0 the retur to scale is ivariability. j j If 0 0 the retur to scale is icrease. j j 35

10 Iteratioal Joural of Maagig Iformatio Techology (IJMIT) Vol.9, No.2, May 207 If 0 0 the retur to scale is decrease. j j To ecourage the istitutio as well as studets better, the ivested istitutio will be asked to submit its related iformatio about retur o scale oce a year for offices i the orgaizatio to poder whether it is ecessary to ivest that school ext year. Supposed that oe uiversity s retur to scale is drop dramatically, apparetly meas that the iputs is far beyod the outputs, it is more wise to stop ad ivest o aother istitutio,forexamplethe20thistitutio. Providedauiversity sreturtoscalegoes rise for 5 years, defiitely the ivestmet duratio for that school is 5 years. 3. CONCLUSIONS The itegratio of AHP, DEA ad MDU methodologies is a hybrid applicatio of soft computig techiques. The aim of the hybrid applicatio is to determie a optimal ivestmet strategy to idetify the schools, the ivestmet amout per school efficietly ad objectively. we utilize AHP (Aalytic Hierarchy Process) to determie the weight of every factor ad rak the schools i the list of cadidate schools accordig to the composite idex of every school calculated from the weight. So we could select schools i the top of the rak to ivest suitable fuds. Furthermore we use DEA (Data Evelope Aalyse) to get chages of scale efficiecy. With this model, we come up with a strategy o what will be both the most efficiet ad accurate way to ivest the Goodgrat Foudatio. Our future work will focus o refiig the model to be more scietific ad more believable. Besides, some factors which are eglected i this model ca be further studied if there is more iformatio available. REFERENCES [] IPEDS UID for Potetial Cadidate Schools. [2] Osma Tayla, Abdallah O. Bafail, Reda M.S. Abdulaal, Mohammed R. ad Kabli, "Costructio projects selectio ad risk assessmet by fuzzy AHP ad fuzzy TOPSIS methodologies", Applied Soft Computig, Vol, 7, 204, pp [3] Pablo Aragoés-Beltráa, Fidel Chaparro-Gozález, Jua-Pascual Pastor-Ferradoc, Adrea Pla- Rubioc, "A AHP (Aalytic Hierarchy Process)/ANP (Aalytic Network Process) -based multicriteria decisio approach for the selectio of solar-thermal power plat ivestmet projects", Eergy, Vol.66, 204, pp [4] Joh S. Liu, Louis Y.Y. Lu, We-Mi Lu. Research frots i data evelopmet aalysis[j]. Omega, 206, 58: [5] Berrittella, M.; A. Certa, M. Eea, P. Zit. "A Aalytic Hierarchy Process for the Evaluatio of Trasport Policies to Reduce Climate Chage Impacts". Fodazioe Ei Erico Mattei (Milao) Jauary [6] ErestH.Forma,SaulI.Gass,The aalytic hierarchy process-a expositio. Operatios Research 200, 49: [7] LIWei,YANGHui.TheApplicatiooftheCCRModelCotaiigNo-Archimedes Dimesioless. Joural of Togre Uiversity,205,7(4): [8] WANG Wei,WANG Zhi-hao,LIU Yu-xi.O DEA Scale Efficiecy of Higher EducatioIputadOutput. ChieseJouralofMaagemetSciece. Vol.2,Special Issue,November,203. [9] Zhi Hua Hu, Jig Xia Zhou, Meg Ju Zhag et al.. Methods for rakig college sports coaches based o data evelopmet aalysis ad PageRak[J]. Expert Systems, 205,32(6)