elif kongar*, mahesh baral and tarek sobh

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





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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379 366329 358

407

584

907

1175

568591

456

571513

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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

0

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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.


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

11

10

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.


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

19

18

17

16

15

14

13 12

11

10

987

6

5

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3

2

1

0

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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 !



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.



June 22-25, 2007June 22-25, 2007



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.



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

OCEANOCEAN

OCEAN – Admin PartOCEAN – Admin Part

http://ocean.bridgeport.edu/ocean/adminpart/adminLoginPage.aspx

http://ocean.bridgeport.edu/ocean/adminpart/adminLoginPage.aspx

elif kongar*, mahesh baral and tarek sobh

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