Data Envelopment Analysis of First-Year Courses at Appalachian … · Data Envelopment Analysis...
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INFORMS Conference on Business Analytics and Operations Research Data Envelopment Analysis of First-Year Courses at Appalachian State University The MathSci O.R. Team Dept of Mathematical Sciences Overview The MathSci O.R. Team Deidre Allworthy, Phillip Bare, Jenna Cantrell, Joseph Castonguay, Taylor Conn, Ashley Cox, Amy Grady, Dustin King, Kimberly Mikeal, Shiloh Moore, J Austin Smith, Tiffany Williams, Jonah Winkler, Steven Yarbrough, and Dr Wm C Bauldry Abstract Data Envelopment Analysis (DEA) is a powerful technique that provides relative comparisons of very different types of depts in an organization. We adapt DEA to analyze distinct activities, rather than departments. We apply DEA to assess relative efficiency of large-enrollment, first-year courses, identifying resource inputs and activity outputs to investigate. Our methodology can be easily adapted to assess relative performance and/or efficiencies of resource utilization for activities across projects in industry and government. For More Information Prof Wm C Bauldry Dept of Mathematical Sciences Appalachian State University Boone, NC 28608 QR vCard The Project Analyze required, first-year, general education classes at Appalachian. We assess four large-enrollment course blocks: I. UCO 1200 First Year Seminar II. BIO 1101 Bio in Society I, BIO 1102 Bio in Society II III. ENG 1000 Expos Writing IV. MAT 1010 Intro to Math, MAT 1020 College Algebra, MAT 1025 Precalculus comparing resource utilization to multiple output production measures. DEA allows us to produce a ranking index based on several diverse inputs and outputs. The Software We use the ‘Optimization’ and ‘simplex’ packages of Maple TM 16, a computer algebra system, to perform the many simplex algorithm runs required by DEA. (Visit www.maplesoft.com for information about Maple.) Background:Data Envelopment Analysis Charnes, Cooper, and Rhodes invented DEA in 1978, basing the technique on “combustion engineering’s ‘efficiency is the ratio of the actual amount of heat liberated . . . to the maximum amount which could be liberated’.” DEA Strengths I Multiple input and multiple output models I Comparison against all combinations of peers I Inputs and outputs can have very different units DEA Weaknesses I Extreme point technique—noisy data causes significant error I Estimates relative, not absolute efficiency I Computationally intensive DEA Linear Program Formulations For each Decision Making Unit DMU o (o = 1..n), with m inputs [x io ] and s outputs [y ro ], define the relative efficiency θ * o by Input-oriented LP Output-oriented LP θ * o = min λ θ subject to n X j=1 x ij λ j 6 θ x io , i = 1..m n X j=1 y rj λ j > y ro , r = 1..s φ * o = max λ φ subject to n X j=1 x ij λ j 6 x io , i = 1..m n X j=1 y rj λ j > φ y ro , r = 1..s with all λ j > 0. Data Envelopment Analysis Diagrammed The efficiency index of a decision making unit is the relative distance DMU R n from the DMU to the efficiency frontier. The efficiency frontier is defined to be the convex hull of the DMU data points. Project Input and Output F actors Input Factors I Number of students enrolled I Number of sections/classes scheduled I Number of seats offered I Beginning student/teacher ratio I Student credit hours generated I Cost (estimate) Output Factors I Percent students successfully completing I Number of students dropping/withdrawing I Mean course GPA factor I Ending student/teacher ratio I Average cost per successful student (estimate) Results and Conclusions Complete Factor Set I Leads to a convex hull with all data points near the frontier — no discrimination among DMUs Subsets of Factors I UCO at 66.9% efficiency index in relation to size inputs versus success & cost outputs; other DMUs at 100% I BIO at 72.9% efficiency index in relation to credit hour inputs versus grade & success outputs; other DMUs at 100% Further Directions Incorporate more granular assessments by: I Extending current blocks; e.g. extending first-year mathematics to all ‘Quantitative Literacy’ courses I Adding each of the four required Perspectives: ‘Aesthetic,’ ‘Historical & Social,’ ‘Local to Global,’ and ‘Science Inquiry’ I Incorporating further, more detailed, cost factors References 1. Cooper, Seiford, and Zhu, eds, Handbook on Data Envelopment Analysis, Kluwer Acad Pub, Boston, 2004. 2. Ramanathan, An Introduction to Data Envelopment Analysis: A Tool for Performance Measurement, Sage Pub, 2003. [email protected] http://mathsci2.appstate.edu/∼wmcb/INFORMS/2012/
Transcript of Data Envelopment Analysis of First-Year Courses at Appalachian … · Data Envelopment Analysis...
INFORMS Conference on BusinessAnalytics and Operations Research
Data Envelopment Analysis of First-YearCourses at Appalachian State University
The MathSci O.R. TeamDept of Mathematical Sciences
OverviewThe MathSci O.R. Team
Deidre Allworthy, Phillip Bare, Jenna Cantrell,Joseph Castonguay, Taylor Conn, Ashley Cox, Amy Grady,Dustin King, Kimberly Mikeal, Shiloh Moore, J Austin Smith,Tiffany Williams, Jonah Winkler, Steven Yarbrough, andDr Wm C Bauldry
AbstractData Envelopment Analysis (DEA) is a powerful techniquethat provides relative comparisons of very different types ofdepts in an organization. We adapt DEA to analyze distinctactivities, rather than departments. We apply DEA to assessrelative efficiency of large-enrollment, first-year courses,identifying resource inputs and activity outputs to investigate.Our methodology can be easily adapted to assess relativeperformance and/or efficiencies of resource utilization foractivities across projects in industry and government.
For More InformationProf Wm C BauldryDept of Mathematical SciencesAppalachian State UniversityBoone, NC 28608 QR vCard
The ProjectAnalyze required, first-year, general education classes atAppalachian. We assess four large-enrollment course blocks:
I. UCO 1200 First YearSeminar
II. BIO 1101 Bio in Society I,BIO 1102 Bio in Society II
III. ENG 1000 Expos WritingIV. MAT 1010 Intro to Math,
MAT 1020 College Algebra,MAT 1025 Precalculus
comparing resource utilization to multiple output productionmeasures. DEA allows us to produce a ranking index based onseveral diverse inputs and outputs.
The SoftwareWe use the ‘Optimization’ and ‘simplex’ packages of MapleTM 16, acomputer algebra system, to perform the many simplex algorithmruns required by DEA.
(Visit www.maplesoft.com for information about Maple.)
Background: Data Envelopment AnalysisCharnes, Cooper, and Rhodes invented DEA in 1978, basing thetechnique on “combustion engineering’s ‘efficiency is the ratio ofthe actual amount of heat liberated . . . to the maximum amountwhich could be liberated’.”
DEA StrengthsIMultiple input and multiple output modelsIComparison against all combinations of peersI Inputs and outputs can have very different units
DEA WeaknessesIExtreme point technique—noisy data causes significant errorIEstimates relative, not absolute efficiencyIComputationally intensive
DEA Linear Program FormulationsFor each Decision Making Unit DMUo (o = 1..n), with m inputs[xio] and s outputs [yro], define the relative efficiency θ∗o by
Input-oriented LP Output-oriented LP
θ∗o = minλ θ
subject ton∑
j=1
xijλj 6 θ xio, i = 1..m
n∑j=1
yrjλj > yro, r = 1..s
φ∗o = maxλφ
subject ton∑
j=1
xijλj 6 xio, i = 1..m
n∑j=1
yrjλj > φ yro, r = 1..s
with all λj > 0.
Data Envelopment Analysis DiagrammedThe efficiency index of a decision making unit is the relative distance
DMU$
Rn
from the DMU to the efficiency frontier. The efficiency frontier isdefined to be the convex hull of the DMU data points.
Project Input and Output Factors
Input FactorsINumber of students enrolledINumber of sections/classes scheduledINumber of seats offeredIBeginning student/teacher ratioIStudent credit hours generatedICost (estimate)
Output FactorsIPercent students successfully completingINumber of students dropping/withdrawingIMean course GPA factorIEnding student/teacher ratioIAverage cost per successful student (estimate)
Results and ConclusionsComplete Factor Set
ILeads to a convex hull with all data points near the frontier— no discrimination among DMUs
Subsets of FactorsIUCO at 66.9% efficiency index in relation to size inputs
versus success & cost outputs; other DMUs at 100%IBIO at 72.9% efficiency index in relation to credit hour inputs
versus grade & success outputs; other DMUs at 100%
Further DirectionsIncorporate more granular assessments by:IExtending current blocks; e.g. extending first-year mathematics
to all ‘Quantitative Literacy’ coursesIAdding each of the four required Perspectives: ‘Aesthetic,’
‘Historical & Social,’ ‘Local to Global,’ and ‘Science Inquiry’I Incorporating further, more detailed, cost factors
References1. Cooper, Seiford, and Zhu, eds, Handbook on Data Envelopment
Analysis, Kluwer Acad Pub, Boston, 2004.2. Ramanathan, An Introduction to Data Envelopment Analysis:
A Tool for Performance Measurement, Sage Pub, 2003.
[email protected] http://mathsci2.appstate.edu/∼wmcb/INFORMS/2012/
