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Are We Accepting the Right Students to Graduate Engineering Programs: Measuring the Success of Accepted Students via Data Envelopment Analysis. Elif Kongar*, Mahesh Baral and Tarek Sobh * Departments of Technology Management and Mechanical Engineering - PowerPoint PPT Presentation
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Elif Kongar*, Mahesh Baral and Tarek SobhElif Kongar*, Mahesh Baral and Tarek Sobh
*Departments of Technology Management and Mechanical EngineeringUniversity of Bridgeport, Bridgeport, CT, U.S.A
2008 ASEE Annual Conference & Exposition2008 ASEE Annual Conference & Exposition
Pittsburgh, PAPittsburgh, PA
June 22-25, 2008June 22-25, 2008
Elif Kongar*, Mahesh Baral and Tarek SobhElif Kongar*, Mahesh Baral and Tarek Sobh
*Departments of Technology Management and Mechanical EngineeringUniversity of Bridgeport, Bridgeport, CT, U.S.A
2008 ASEE Annual Conference & Exposition2008 ASEE Annual Conference & Exposition
Pittsburgh, PAPittsburgh, PA
June 22-25, 2008June 22-25, 2008
Are We Accepting the Right Students to Graduate Engineering Programs: Measuring the Success of Accepted Students via Data Envelopment Analysis
UB SOE MS Enrollment Fall 2000 - 2007
Sources: 1. Office of the President, University of Bridgeport, October 2007
# of Available Dual Degree Programs: 16# of Available Concentration Areas / Graduate Certificate Programs: 34
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Fall 2000 Spring 2001 Fall 2001 Spring 2002 Fall 2002 Spring 2003 Fall 2003 Spring 2004 Fall 2004 Spring 2005 Fall 2005 Spring 2006 Fall 2006 Spring 2007 Fall 2007
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Motivation – I : Difficulties in admission procedure due to increasing number of students in the SOE at UB.Motivation – I : Difficulties in admission procedure due to increasing number of students in the SOE at UB.
# of Available Dual Degree Programs: 16# of Available Concentration Areas / Graduate Certificate Programs: 34
Being able to admit students in less than 5 minutes: Priceless
UB SOE Enrollment 2002 - 2008
Motivation – IIMotivation – IILack of literature to suggest a solution for customized curriculum.
Moore (1998) - an operational two-stage expert system to examine the admission decision process for applicants to an MBA program, and predict the degree completion potential for those actually admitted.
Nilsson (1995) - differences in the predictive relationships between the scores of the Graduate Record Examination (GRE) and the graduate grade point average, and the scores of the Graduate Management
Admission Test (GMAT) and the graduate grade point average.
Landrim et al. (1994) - a value tree diagram for fifty-five graduate institutions offering the Ph.D. degree in psychology. The authors used this diagram to indicate the relative weight of admission factors used in
the decision making process.
Introduction – Data Envelopment AnalysisIntroduction – Data Envelopment Analysis
DM UA pplicant
E valuation
x1
y1
y1 = # years o f wo rk experiencey2 = G R E -Q sco re
x1 = # years till B S co m pletio nInput:
O utputs :
DEA system
y2
x2 = funding allocation ($)
(year)(year)
(number)
y3 = compatibility of research (IN)
Efficiency = Output/Input
Years of W ork Experience
GR
E S
core
(Q
uant
itativ
e)
0
Efficiency of Candidate BOB/OV = app. 70%
A simple numerical DEA exampleA simple numerical DEA example
x1 y1 y2
A
B
C
100
100
100
0
2
12
800
500
450Cand
idat
es
OutputInput
V
A (0,800)
B (2,500) C (12,450)
y1 = # years o f wo rk experiencey2 = G R E -Q sco re
x1 = # years till B S co m pletio nInput:
O utputs :
Efficiency Frontier
Two DEA ModelsTwo DEA Models
I. DEA Model ITo rank the applicants according to: • e1 = number of below-B grades in math-related/technical
courses in the BS transcript of the applicant,• e2 = number of semesters to complete the BS degree,• e3 = BS GPA of the applicant,• e4 = TOEFL score of the applicant,• e5 = GRE-Q score of the applicant,• e6 = number of years of work experience of the applicant.
Two DEA ModelsTwo DEA Models
DEA Model ITo rank the applicants according to: • e1 = number of below-B grades in math-related/technical
courses in the BS transcript of the applicant,• e2 = number of semesters to complete the BS degree,• e3 = BS GPA of the applicant,• e4 = TOEFL score of the applicant,• e5 = GRE-Q score of the applicant,• e6 = number of years of work experience of the applicant.
e1 = number of below-B grades in math-related/technical courses in the BS transcript of the applicant, e2 = number semesters that the applicant spent to complete the BS degree, e3 = BS GPA of the applicant, e4 = TOEFL score of the applicant, e5 = GRE-Q score of the applicant, e6 = number of years of work experience of the applicant.
MS Computer Science Application Data (Fall 2004)MS Computer Science Application Data (Fall 2004)
Source: Office of Admissions, University of Bridgeport, 2008
37 Students
DMU # e1 e2 e3 e4 e5 e6 DMU # e1 e2 e3 e4 e5 e6
1 8 8 3.22 477 640 0 20 17 8 3.11 560 610 0
2 11 8 3.2 507 770 0 21 12 8 3.32 610 730 0
3 0 8 2.37 574 693 0 22 6 6 3.68 574 693 2
4 5 6 3.14 490 750 0 23 0 6 3.4 574 693 5
5 0 8 3.98 553 800 0 24 12 8 3.24 577 730 0
6 18 8 2.92 677 790 1 25 9 8 3.04 583 580 0
7 20 10 2.97 633 780 0 26 0 8 2.97 560 760 0
8 8 8 3.1 563 660 2 27 14 8 3.03 550 730 0
9 2 8 3.56 593 800 0 28 7 8 3.34 560 640 0
10 23 8 2.98 523 660 2 29 9 8 3.34 550 620 0
11 15 8 3.24 563 700 0 30 11 8 3.07 647 630 0
12 0 6 3.77 597 600 0 31 7 8 3.52 563 670 0
13 6 8 3.41 593 660 0 32 1 6 3.38 653 760 7
14 1 8 3.85 600 770 0 33 3 8 3.67 560 610 0
15 11 8 3.33 550 570 0 34 2 6 3.5 574 693 8
16 1 8 3.68 480 693 2.5 35 0 8 3.44 587 770 0
17 0 6 4 603 660 0 36 10 8 3 567 540 0
18 1 8 3.92 643 800 0 37 18 8 2.57 547 670 0
19 9 8 3.37 627 710 0 Ave. 7.5 7.7 3.3 574.1 692.8 0.8
Relative Efficiency Scoresand Ranks of Each Candidate
Relative Efficiency Scoresand Ranks of Each Candidate Rank DMU# TE I Rank DMU# TE I
1 34 1.000 20 21 0.727 1 32 1.000 21 27 0.720 1 23 1.000 21 24 0.720 1 17 1.000 23 31 0.711 5 12 0.990 24 13 0.703 6 4 0.987 25 11 0.703 7 22 0.986 26 33 0.694 8 5 0.868 27 28 0.677 9 35 0.833 28 25 0.671
10 18 0.823 29 8 0.667 11 26 0.823 30 1 0.666 12 14 0.799 31 29 0.666 13 9 0.790 32 15 0.663 14 6 0.780 33 37 0.661 15 2 0.760 34 20 0.657 16 3 0.750 35 36 0.655 17 30 0.743 36 10 0.655 18 16 0.739 37 7 0.616 19 19 0.728 Average 0.774
3736 35 34
33
32
31
3029
28
27
2625
24
23
2221
20
19
18
17
16
15
14
13 12
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987
6
5
4
3
2
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.7 0.8 0.9 1TE I
TE
II
DEA I - Technical Efficiencies, Min, Mean, Max.DEA I - Technical Efficiencies, Min, Mean, Max.
Driven by the number of below-B grades.
Average technical efficiency = 77.4%
B.S. degree completion in identical number of semesters (6).
High GPAs, GRE-Q scores, years of work experience, significantly low numbers of below-B grades in
math-related/technical courses.
Two DEA ModelsTwo DEA Models
DEA Model IITo rank the applicants according to: • t1 = number of below-C grades in the M.S. transcript of
the M.S. candidate,• t2 = GPA of the M.S. candidate,• t3 = application status for the Curricular Practical
Training (CPT) or Optional Practical Training (OPT).
MS Computer ScienceApplication Data (Fall 2004)MS Computer ScienceApplication Data (Fall 2004)
Source: Office of Admissions, University of Bridgeport, 200837 Students
DMU # t1* t2 t3 t4 DMU # t1 t2 t3 t4
1 1 3.12 2 2 20 0 2.34 1 1
2 0 3.21 2 2 21 0 3.42 2 2
3 0 0.00 1 1 22 0 3.38 2 2
4 0 3.03 2 1 23 3 2.07 1 1
5 0 4.00 1 1 24 0 2.67 1 1
6 0 3.58 2 2 25 0 3.58 2 2
7 0 3.49 2 2 26 0 3.24 2 2
8 0 3.56 2 1 27 0 2.00 1 1
9 0 3.46 1 2 28 2 0.00 1 1
10 2 2.40 1 1 29 0 3.14 2 2
11 0 3.18 2 2 30 0 3.43 1 2
12 0 3.27 2 2 31 0 2.45 1 1
13 0 3.30 2 2 32 0 3.72 1 1
14 0 3.45 2 2 33 0 2.89 1 1
15 0 3.11 2 2 34 0 3.37 2 2
16 0 3.21 2 2 35 0 3.70 2 2
17 0 3.58 2 2 36 0 3.15 1 2
18 0 3.00 1 1 37 0 3.58 2 2
19 0 3.43 2 2 Ave. 0.2 3.01 1.6 1.6 *All zero values are changed to a significantly low
positive value of 10-5 to avoid division by zero.
t1 = number of below-C grades in the M.S. transcript of the
M.S. candidate,t2 = GPA of the M.S. candidate,
t3 = application status for the Curricular Practical Training (CPT) or Optional Practical
Training (OPT).
3736 35 34
33
32
31
3029
28
27
2625
24
23
2221
20
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987
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0
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0.5
0.6
0.7
0.8
0.9
1
0.6 0.7 0.8 0.9 1TE I
TE
II
DEA II - Technical Efficiencies, Min, Mean, Max.DEA II - Technical Efficiencies, Min, Mean, Max.
Driven by the lack of OPT or CPT applications and failure to graduate.
Average technical efficiency = 82.2%
High GPA & graduation.
Comparing DEA I & II – Establishing a PatternComparing DEA I & II – Establishing a Pattern T E I = 1 E f f ic ient D M U s
T E I < 0.774 D M U s
TE
II =
1 E
ffici
ent D
MU
s TE
II < 0.822 D
MU
s
34 , 17
32
37, 36, 2, 7 , 8 ,11, 13, 15, 16,30, 19, 29, 21,
25
23
33, 24, 31, 20,27, 3 , 1 , 10, 28
35, 4 , 5 , 6 , 9 , 12, 14,22, 26
18
50%
56% 39%
9%
Proposed DEA application detects the efficient DMU more successfully compared to the ones that are below the average.
Conclusions Conclusions
DEA allows introduction of intangible and out-of-system indicators.
Allows these inputs and outputs to be expressed in different units of measurement.
Can accommodate multiple inputs and multiple outputs.
Does not require an assumption of a functional form relating inputs to outputs.
Quality of data is important.
TE is affected by the performance indicators.
Additional criteriaUniversity rankingProblem statementFinancial statement# publications/projectsQuality of publications/projectsand others
WeightAutomated model (DEA Solver Pro v.5.0)
Database I/OStatistics collection
Predict and compare the degree completion for those actually admitted
Future ResearchFuture Research
Thank you !
Elif Kongar*, Mahesh Baral and Tarek SobhElif Kongar*, Mahesh Baral and Tarek Sobh
*Departments of Technology Management and Mechanical EngineeringUniversity of Bridgeport, Bridgeport, CT, U.S.A
We would like to acknowledge the following individuals that We would like to acknowledge the following individuals that
contributed their time and, more importantly, their innovative ideas to thiscontributed their time and, more importantly, their innovative ideas to this
project.project.
Audrey Ashton-Savage, Vice President of Enrollment Management; Bryan Gross Audrey Ashton-Savage, Vice President of Enrollment Management; Bryan Gross and Isabella Varga, Office of Admissions.and Isabella Varga, Office of Admissions.
2008 ASEE Annual Conference & Exposition2008 ASEE Annual Conference & Exposition
Pittsburgh, PAPittsburgh, PA
June 22-25, 2007June 22-25, 2007
Elif Kongar*, Mahesh Baral and Tarek SobhElif Kongar*, Mahesh Baral and Tarek Sobh
*Departments of Technology Management and Mechanical EngineeringUniversity of Bridgeport, Bridgeport, CT, U.S.A
We would like to acknowledge the following individuals that We would like to acknowledge the following individuals that
contributed their time and, more importantly, their innovative ideas to thiscontributed their time and, more importantly, their innovative ideas to this
project.project.
Audrey Ashton-Savage, Vice President of Enrollment Management; Bryan Gross Audrey Ashton-Savage, Vice President of Enrollment Management; Bryan Gross and Isabella Varga, Office of Admissions.and Isabella Varga, Office of Admissions.
2008 ASEE Annual Conference & Exposition2008 ASEE Annual Conference & Exposition
Pittsburgh, PAPittsburgh, PA
June 22-25, 2007June 22-25, 2007
Are We Accepting the Right Students to Graduate Engineering Programs: Measuring the Success of Accepted Students via Data Envelopment Analysis
RA: A statistical technique used to find relationships between variables for the purpose of predicting future values.
Regression AnalysisRegression Analysis
x1 = 19.04651 – 0.02465x2
DEA “orientation”DEA “orientation”
• Input-oriented DEA models define efficiency as “the least input for the same amount of output”
• Output-oriented DEA models define it as “the most output for the same amount of input”.
• Other considerations:• # of DMUs = App. 2 to 5 times of the sum of Input and
Output variables• Input and output selection
• Data envelopment analysis (DEA) is a widely applied linear programming-based technique.
• Low divergence low complexity • Aim is to evaluate the efficiency of a set of decision-
making units.• DEA has mostly been used for benchmarking and for
performance evaluation purposes.• A DEA approach to measure the relative efficiency of end-
of-life management for iron in different countries.
Justification of Method SelectionJustification of Method Selection
Advantages of DEAAdvantages of DEA
• Can accommodate multiple inputs and multiple outputs• Allows these inputs and outputs to be expressed in different
units of measurement.• It doesn't require an assumption of a functional form relating
inputs to outputs. • DMUs are directly compared against a peer or combination of
peers.• Efficient units form the “efficient frontier” and inefficient units
are enveloped by this frontier providing information on their improvement potential.
max
m
jjpj
s
kkpk
xu
yv
1
1
s. t.
1
1
1
m
jjij
s
kkik
xu
yv
DMUs i
0, jk uv
k , j.
( 1 )
Data Envelopment Analysis ModelData Envelopment Analysis Model
where,k = 1 to s,j = 1 to m,i = 1 to n,
yki = amount of output k produced by DMU i,xji = amount of input j produced by DMU i,
vk = weight given to output k,uj = weight given to input j.
max s.t.
0 i
jiijp xx
Inputs j
0 i
kiikp yy
Outputs k
0i
DMUs i.
( 4 )
Dual Output-oriented CRS ModelDual Output-oriented CRS Model
Collect Application
Materials
Application packagecompleted?
Yes
No
InputApplicationDatabase
Notify the Candidates thatare Not Accepted
Refer Application to theCommittee
Accepted? No
Decision/Suggestions bythe Committee
Yes
Notify Fully/ConditionallyAccepted Candidates
Will be substituted by theproposed DEA model
Fliter out the unqualifiedapplications
Notify the Candidates thatare Not Accepted
Send Confirmation E-mail
Simplified schematic diagram of the application evaluation and decision making process
Simplified schematic diagram of the application evaluation and decision making process
OCEAN – Admin PartOCEAN – Admin Part
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