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

International Journal of Managing Information Technology (IJMIT) Vol.9, No.2, May 2017
DOI : 10.5121/ijmit.2017.9203 27
AN AHP(ANALYTIC HIERARCHY PROCESS)-BASED
INVESTMENT STRATEGY FOR CHARITABLE
ORGANIZATIONS OF GOODGRANT FOUNDATION
Xue-ying Liu, Jian-sheng Yang, Xiao-yan Fei and Ze-jun Tao
College of Science, Shanghai University, Shanghai, 200444, China
ABSTRACT
This paper provides the optimal investment strategy for the Goodgrant Foundation. To determine the
schools to be invested, firstly we find the factors about improving students’ educational performance,
including urgency of student’s needs, school’s demonstrate potential for effective use of private funding,
the reputation of school, and return on investment etc; secondly, we utilize AHP (Analytic Hierarchy
Process) to determine the weight of every factor and rank the schools in the list of candidate schools
according to the composite index of every school calculated from the weight. To confirm the investment per
school and obtains the investment duration time, we use DEA (Data Envelope Analyse) to get changes of
scale efficiency; and then according to the change trend, we determine time duration of investment and
effective utilization of private funding, which is the factor together with student population affecting the
investment amount for per school. It is helpful to make a better decision on investing universities, We are
convinced that our research is promising to benefit all sides of students, schools and Goodgrant.
KEYWORDS
AHP, DEA, Educational Performance, Investment Strategy
1. INTRODUCTION
Universities and colleges are places where young students gain valuable knowledge, resources
and opportunities before they step into the society. That is why many foundations are willing to
invest on undergraduates to help improve their educational performance. With so many
universities and colleges in American, it is necessary for us to carry out a method about how to
determine an optimal investment strategy to identify the schools, the investment amount per
school efficiently and objectively. How to distribute the fund is exactly the key. It is a multi-
aspect evaluate task including the urgency of students’ needs, school’s demonstrate potential for
effective use of private funding, the reputation of school, return on investment etc. Mean while,
the time duration that the organization’s money have the highest likelihood of producing a strong
positive effect on student performance should also be a primary consideration.
OtherlargeandknowngrantorganizationssuchasGatesFoundationandLuminaFoundation show the
current way to investigate the quailfication which mainly concentrates on the low income of
students’ families and potential of universities. These models will take the ability of using the
funding and rate of return into account, and obtain approximate investment duration time and
return of investments oth at the Good grant Foundation can provide the assistance best to not only
students but also schools and foundation itself.
The analytic hierarchy process (AHP)[2-4] is a structured technique for organizing and analyzing
complex situation. It is based on mathematics and psychology. Rather than prescribe a “correct”
decision, the AHP helps decision makers find one that best suits their goal and their
understanding of the problem[5-6]. It provides a comprehensive and rational framework for

28
structuring a decision problem, for representing and quantifying its elements, for relating those
elements to overall goals, and for evaluating alternative solutions.
This paper provides the optimal investment strategy for the Goodgrant Foundation by AHP
method[2]. It helps improv educational performance of undergraduates in United States and make
them graduate successfully, live a good life in the future. The rest of this paper is organized as
follows: in Section 2, wepresentourmodel approach in detail, including the analytical hierarchy
process model anddata envelope analysemodel.Conclusions are provided in the last Section.
2. MODEL DESIGN
2.1 THE ANALYTICAL HIERARCHY PROCESS MODEL
By using cluster analysis, We group all the colleges corecard data into urgency of students’needs,
school’s demonstrate potential for effective use of private funding, the reputation of school,
return on investment 4 groups. Meanwhile urgency of students’ needs contains share of part-time
undergraduates, median debt of completers and average net price; School’s demonstrate potential
for effective use of private funding contains percentage of undergraduates who have received a
PellGrant, percent of all federal under graduate students receiving a federal student loan and 3-
year repayment rate; The reputation of school includes predominant degree awarded, discipline
distribution and structure and whether it is operating with other institutions; Return on investment
includes Median earnings of students 10 years after entry, share of students earning over
25,000dollar/year 6 years after entry. The dates of 2936 universities are in Table 1.
Table 1: Dates of 2936 Universities
2.1.1 THE ESTABLISHMENT OF A HIERARCHY
The problem of the case can be divided into three layers in order.

29
2.1.2 THE WEIGHTS OF LAYER C IN LAYER O
Considering the relative importance of C1 compared with C2, C3, C4; we might arrive at the
following pair wise comparison matrix.
1 3 5 5
1
1 1 2
3
1
1 1 2
5
1 1 1
1
5 2 2
A
 
 
 
 
 
 
 
 
 
 
The maximum eigenvalue λ1 = 4.05, and we can get the corresponding normalized eigenvector
w1 = (0.58,0.17,0.16,0.09).
2.1.3 CONSISTENCY TEST
Consistency Index
max
1
n
CI
n
 


when n = 4,λ1 = 4.05,CI = 0.016, Random Consistency Index RI = 0.9,it can be get from the table
below(Table 2).
Table 2: Random Consistency Index
Consistency Ratios
CI
CR
RI

When RI = 0.9, CR = 0.018 < 0. 1 meet the inspection.

30
2.1.4 THE WEIGHTS OF LAYER P IN LAYER C
Considering the relative importance of P1 compared with P2,P3;P4 compared with P5,P6;P7
compared with P8,P9;P10 compared with P11; We might arrive at the following pairwise
comparison matrix:
1
1
1 1
3
3 1 3
1
1 1
3
B
 
 
 
  
 
 
 
 
2
1
1 1
3
1
1 1
3
3 3 1
B
 
 
 
 
  
 
 
 
 
3
1 3 6
1
1 5
3
1 1
1
6 5
B
 
 
 
 
 
 
  
 
4
3
1
7
7
1
3
B
 
 
 
 
 
 
The maximum eigen value λ2 = 3,λ3 = 3,λ4 = 3.10,λ5 = 2 and we can get the corresponding
normalized eigen vector
w1 = (0.2,0.6,0.2)T
w2 = (0.2,0.2,0.6)T
w3 = (0.635,0.287,0.078)T
w4 = (0.3,0.7)T
After normalization, we can weight vector
4
( )
2 2
1
0. 08K
i
CR CR

 
2.1.5 THE WEIGHTS OF LAYER P IN LAYER O
( ) ( ) ( ) ( )
1 2
( , . . . . , ) ( 1,2,3,4)k k k k
n
W k   
(1) ( 2) ( 3) ( 4)
2 11 4
[ , , , ]W W W W W 


    (1) (2) (3) (4)
2 1 1
[ , , , ] (0.115,0.345,0.115,0.035,0.035,0.10 6,0.099,0.045,0.012,0.03,0.065)W WW W W W W W
1 2 0. 098 0. 1CR CR CR   
2.1.6 DATA NORMALIZATION METHOD
In order to reconcile all kinds of indicator sin one assessment system, we apply Min Max
Normalization to normalize the indicators that mentioned in the database. This helps us to process
data in various dimension. Our process of data normalization is as following formula



* mi n
max mi n
x
x
0. 0010 0. 0007 0. 0004 0. 0004 0. 0006 0. 0003 0. 0004 0. 0000 0. 0000 0. 0004 0. 0004
0. 0007 0. 0008 0. 0003 0. 0005 0. 0005 0. 0002 0. 0004 0. 0000 0. 0000 0. 0003 0. 0003
0. 0011 0. 0007 0. 0003 0. 0006 0. 0006 0. 0002 0. 0003 0. 0000 0. 0000 0. 0003 0. 0003
s 0. 0001 0. 0008 0. 0007 0. 0004 0. 0006 0. 0003 0. 0004 0. 0000 0. 0000 0. 0004 0. 0004
0. 0010 0. 0004 0. 0006 0. 0002 0. 0000 0. 0000 0. 0003 0. 0000 0. 0000 0. 0003 0. 0002
0. 0001 0. 0005 0. 0005 0. 0005 0. 0006 0. 0003 0. 0004 0. 0000 0. 0000 0. 0004 0. 0004



 
 
 
 
 
 
 
 
 
 

31
2.1.7 COMPREHENSIVE RANK
We can ﬁgure out the following formula to quantize the satisfaction of Goodgrant to the school.
1
( 1, ,2936)
n
i i j j
j
D b W i

  
Lastly, we utilize Analytic Hierarchy Process (AHP) to determine the weight of
everyfactorandranktheschoolsinthelistofcandidateschoolsaccordingtothecomposite index of every
school calculated from the weight. Than we can select schools in the top of the rank to invest
suitable funds.

32
2.2 DATA ENVELOPE ANALYSE
2.2.1 BASIC CONCEPTION OF DEA
After assessing the educational performance of all post secondary colleges and universities,in
accordance with the rank,we select 200 universities who are most deserving grants. Then it comes
to the question of the amount of money distributed to per school. We consider the ability of
effective using of private funding and the population as the main factors. To quantize the funding
use capacity , we evaluate the relative efficiency of the same type of output and input Decision
Making Unit(DMU) and employ the Date Envelopment Analysis (DEA)[8-9].
Parameter Assumption :X: input index ,Y : output index , to a certain project we assume that
there are s decision making units per unit of which has m kinds of inputs and n kinds of inputs ,
weight coefficient correspondingly V=(v1,v2,v3,…,vm)T
,U=(u1,u2,u3,…,um)T
,every unit hasits own
efficiency evaluation goals(h), hj = uYj/vXj,we can always choose proper weight coefficient which
satisfy hj1,j = 1,2,,s.
In order to estimate the efficiency of DMU, weight coefficient correspondingly v ,u as variable ,
aim at the efficiency index of DMU,restraint by all efficiency indexes ,develop the fractional
programming model as followed:
1
1
n
r r k
r
k m
i i k
i
u y
Max h
v x





1
1
. . 1




n
r r k
r
m
i i k
i
u y
st
v x
In which
0r
u     0i
v
Let r r
U t u  i i
V t v  0r
U   0i
V   after Charnes-Cooper transform we get C2
R
linear programming model
1
n
k r t k
r
Max h U y

  1
. . 1


m
i i k
i
st v x
1 1
0
n m
r r j i i j
r i
U y v x
 
  
Introduceslackvariables-andsurplusvariables+andgettheCCRDualitylinearlayout model
[ ( )]Max e s e s     
 
0
1
. .
n
j j j
r
st x s x 

 

33
0
1
n
j j j
j
y s y 

 
In which: θk presents the potential quota of all inputs possibility of equal proportion reduction.
eΛT
,eT
present m dimension unit column vector and n dimension unit column vector. ε presents
The Archimedes dimensionless, which is smaller than any number bigger than zero.
2.2.2 THE SOURCE OF SAMPLE DATA
After disposal data we choose the amount of Pell Grant and federal student loan as input indexes,
the amount of earnings of students working and not enrolled 10 years after entry and high in
come students 6years after entry as output indexes. The processed data was showed in the
following table(Fig4).
2.2.3 ESTABLISHMENT OF MODEL
CCR Model
1 1 2 2 1 2
78403800 31492914Max h U y U y u u   
1 2 1 2
78403800 31492914 6810564. 51 5436272. 18 0u u v v   
1 2 1 2
14847200 7072340. 41 1940932. 15 1983377. 62 0   u u v v
1 2 1 2
12593500 5532753. 92 1943720. 06 1983273. 33 0u u v v   
1 2 1 2
279864000 95493619. 73 891828. 08 13107856. 32 0u u v v   
1 2 1 2
118895000 24518661. 35 4553961. 46 1364384. 63 0u u v v   
1 2 1 2
7433400 28817188. 48 8144706. 34 7008249. 55 0u u v v   
1 2 1 2
, , , 0u u v v 

34
BCC model
Min
1 2 199 200 1
78403800 14847200 118895000 74334000 78403800s    
     
1 2 199 200 2
31492914. 41 7072340. 41 2451866. 35 28817188.48 31492914. 41
      s    
1 200 1
6810564. 51 8144706. 34 6810564. 51s  
   
1 200 2
5436272. 18 7008249. 55 5436272. 18
    s 
1 2 200
1     
1 2 200
, , , , , 0s s    

2.2.4 CALCULATING
We adopt calculating software Deap Version 2.1 developed by professor Coelli to process the
sample data on the table and get the efﬁciency of DMU(θ) and slack variable(s−
,s+)
.
Figure 5: computational results of Deap Version

35
2.2.6 APPLICATION
To balance the amount of money for per school. Whether the school can maximize the value of
funding it receives is the major consideration factor plus the population effect. We divide the two
factors as 7:3, and making the ﬁnal decision according to each weighting. Part of the table has
been showed on the below(Fig.6).
2.2.7 FURTHER THINK
To decide the duration that the organization’s money should be provided, the main aspect we
consider is to stimulate the highest likelihood of producing a strong effect on student
performance. So we consider the change condition of the return to scale in DMU:
If 0
0
1
1
1
n
j
j

 
 the return to scale is invariability.
If 0
0
1
1
1
n
j
j

 
 the return to scale is increase.

36
If 0
0
1
1
1
n
j
j

 
 the return to scale is decrease.
To encourage the institution as well as students better, the invested institution will be asked to
submit its related information about return on scale once a year for offices in the organization to
ponder whether it is necessary to invest that school next year. Supposed that one university’s
return to scale is drop dramatically, apparently means that the inputs is far beyond the outputs, it
is more wise to stop and invest on another institution,forexamplethe201thinstitution.
Providedauniversity’sreturntoscalegoes rise for 5 years, definitely the investment duration for that
school is 5 years.
3. CONCLUSIONS
The integration of AHP, DEA and MDU methodologies is a hybrid application of soft computing
techniques. The aim of the hybrid application is to determine an optimal investment strategy to
identify the schools, the investment amount per school efficiently and objectively. we utilize AHP
(Analytic Hierarchy Process) to determine the weight of every factor and rank the schools in the
list of candidate schools according to the composite index of every school calculated from the
weight. So we could select schools in the top of the rank to invest suitable funds. Furthermore we
use DEA (Data Envelope Analyse) to get changes of scale efficiency. With this model, we come
up with a strategy on what will be both the most efficient and accurate way to invest the
Goodgrant Foundation. Our future work will focus on refining the model to be more scientific
and more believable. Besides, some factors which are neglected in this model can be further
studied if there is more information available.
REFERENCES
[1] IPEDS UID for Potential Candidate Schools. http://www.comap-
math.com/mcm/ProblemCDATA.zip.
[2] Osman Taylan, Abdallah O. Bafail, Reda M.S. Abdulaal, Mohammed R. and Kabli, "Construction
projects selection and risk assessment by fuzzy AHP and fuzzy TOPSIS methodologies", Applied
Soft Computing, Vol, 17, 2014, pp. 105-116.
[3] Pablo Aragonés-Beltrána, Fidel Chaparro-González, Juan-Pascual Pastor-Ferrandoc, Andrea Pla-
Rubioc, "An AHP (Analytic Hierarchy Process)/ANP (Analytic Network Process)-based multi-
criteria decision approach for the selection of solar-thermal power plant investment projects", Energy,
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[4] John S. Liu, Louis Y.Y. Lu, Wen-Min Lu. Research fronts in data envelopment analysis[J]. Omega,
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[5] Berrittella, M.; A. Certa, M. Enea, P. Zit. "An Analytic Hierarchy Process for the Evaluation of
Transport Policies to Reduce Climate Change Impacts". Fondazione Eni Enrico Mattei (Milano)
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[8] WANG Wei,WANG Zhi-hao,LIU Yu-xin.On DEA Scale Efficiency of Higher
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[9] Zhi‐Hua Hu, Jing‐Xian Zhou, Meng‐Jun Zhang et al.. Methods for ranking college sports coaches
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