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Data Envelopment Analysis: Introduction and an Application to University AdministrationByEmmanuel Thanassoulis,Professor in Management Sciences Aston University,Birmingham, [email protected]
Outline
Introduction to DEA: a graphical example
DEA models: mathematical generalisation
An Application of DEA to University Administration
DEA: a method for comparing homogeneous operating units such as schools, hospitals, police forces, individuals etc on efficiency.
• DMU• Decision
Making Unit
• Inputs • The
operating units typically use resources
• Outputs• The operating units
typically produce or otherwise enable some useful outcomes (e.g. goods or services such as education or health outcomes)
•DEA makes it possible to compare the operating units on the levels of outputs they secure relative to their input levels.
•DMUs Inputs and Outputs
Graphical Example on DEA
What is the efficiency of Hospital HO1 in terms of scope to reduce doctor andnurse numbers?
DMU Doctors NursesOutpatients(
000)
H01 25 60 1
H02 10 50 1
H03 28 16 1
H04 30 40 1
H05 40 70 1
H06 30 50 1
DMU Doctors Nurses Outpatients
H01 30 72 1200H02 10 50 1000H03 35 20 1250H04 33 44 1100H05 52 91 1300H06 24 40 800
• Normalise inputs
per 1000 outpatients
We assume that interpolation of hospitals yields input output levels which are feasible in principle.
Example: take 0.5 of the input-output levels of hospital 2 and 0.5 of the input-output levels of hospital 3 and combine:
Deploy the Interpolation Principle to Create a set of Feasible ‘hospitals’
DMU Doctors NursesOutpatients
(000)
H01 25 60 1
H02 10 50 1
H03 28 16 1
H04 30 40 1
H05 40 70 1
H06 30 50 1
1000
33
19
1000
16
28
5.0
1000
50
10
5.0 • 0.5 HO2 +0.5HO3 =
Feasible units (hospitals)
1000
33
19
1000
16
28
5.0
1000
50
10
5.03 Hospital 0.5 2 Hospital 0.5
DMU Doctor Nurse Outpatient
H01 25 60 1000
H02 10 50 1000
H03 28 16 1000
H04 30 40 1000
H05 40 70 1000
H06 30 50 1000
Feasible units (Hospitals) The interpolation assumption means that 19 doctors and 33
nurses, though observed at no hospital, are capable of handling 1000 outpatients.
• number of doctors 19.• number of nurses 33
• andoutpatients 1000.
• Further, any hospital is also feasible if its input -output levels satisfy
A linear programming approach
• H02 and H03 are efficient peers to H01.
• Efficient Doctor-Nurse levels for H01 are (16.1, 38.5)
Hos D’trs N’rsesOutpati
ents
H01 25 60 1000
H02 10 50 1000
H03 28 16 1000
H04 30 40 1000
H05 40 70 1000
H06 30 50 1000
• doctors: 25 l1 + 10 l2 + 28 l3 + 30 l4 + 40 l5 + 30 l6 • nurses : 60 l1 + 50 l2 + 16 l3 + 40 l4 + 70 l5 + 50 l6 • outpatients : 1000 l1 + 1000 l2 + 1000 l3 + 1000 l4 + 1000 l5 + 1000 l6 • l1, l2, l3 ,l4 ,l5, l6>= 0 .
≤ 25 θ ≤ 60 θ ≥1000
• Min θ• Such that:
%6464.060
5.38
25
5.16
nurse Actual
nurses ofTarget doctors Actual
doctors ofTarget
H01 of efficiency relative The
SAMPLE AREAS WHERE DEA HAS BEEN USED
Banking
Education
Regulation of ‘natural’ monopolies (e.g. water distribution, electricity, gas)
Tax collection
Courts
Sales forces (e.g. insurance sales teams)
TYPES OF ANALYSIS
Relative efficiency measure; Identification of efficient exemplar units; Target setting. decomposing efficiency in layered data (pupil, school, type of school etc);Decomposing productivity changes over time into those attributable to the unit and those to technology shift (Malmquist Indices) Identifying the increasing/decreasing returns to scale;Measuring scale elasticity; Identifying most productive scale size;
ASSESSING EFFICIENCY AND PRODUCTIVITY IN UK UNIVERSITY ADMINISTRATION1999/00 TO 2004/05.
Prof. Emmanuel [email protected]
Aim of this project
To identify units with cost-efficient good quality administrative services and disseminate good practice;
To assess changes in the productivity of UK university administration over time (1999/00 to 2004/5).
Motivation for the Study
Expenditure on Administration and Central Services is about 20% of total HEI expenditure in the UK
Hence expenditure on administration is substantial and competing with direct expenditure on academic activities.
Questions to be addressed:
Are efficiency savings possible?
Is there a trade-off between expenditure and quality of service in administration ?
Has there been any change over time in productivity of administrative services in UK Higher Education Institutions (HEIs)?
The Assessment MethodWe opted for Data Envelopment Analysis (DEA).
This is a linear programming based benchmarking method.
It identifies cost-efficient benchmark units and then assesses the scope for savings at the rest of the units relative to the benchmarks.
CAS 14
CAS 2
CAS 8
CAS 5
CAS 12
CAS 6
CAS 11
CAS 10CAS 9
CAS 13
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 2 4 6 8
Students per £CAS spend
Res.
Gra
nts
per
£C
AS
spend
The virtual benchmark VBM6 offers the top levels of research grants and students when keeping to the mix of research grants to students of CAS6.
VBM6
The distance from CAS6 to VBM6 reflects the scope for savings at CAS 6.
DEA is illustrated in the graph below. An ‘efficient boundary’ is created from benchmark units (CAS12 and CAS2).
Unit of Assessment
The unit of assessment includes core CAS and administration devolved away from the centre;
It excludes Estates, Libraries, Residences and catering.
The Unit of Assessment
Initial consultations with senior administrators and academics suggested the following conceptual framework for the unit of assessment:
Support for research
Support for non admin staff
Support for students
Assessments were carried out by setting the Admin costs against the Measures of Admin Volume shown (at university level).
INPUT – OUTPUT SET
ADMIN COST MEASURE(S) (INPUTS):
ACTIVITY VOLUME MEASURES (OUTPUTS):
Admin staff costsStudentsMeasure used: Total income from Students
Staff Measure used: Non-administrative staff cost
OPEX on administrationResearch grants and other services rendered: Measure used: Income from these sources
Research volume and quality Measure used: QR component of HEFCE income
Input – Output Set
Model Specification
VRS model – Input oriented
Outliers have been re-scaled to be on the boundary formed by the non-outlier units;
A balanced panel between the first (1999/00) and the last (2004/5) year is reported upon here.
100 universities are therefore included in the assessment reported here.
Findings at University Level - illustration
The efficiency here is a percentage. It means the observed admin staff costs can be reduced each year to the percentage indicated above (e.g. 57.57% in 1999/00).
So relative to benchmark institutions for student income, non admin staff expenditure and research income, administrative staff costs could be about half.
The scope for efficiency savings on Operating Expenditure is less than for administrative staff, at about 25% - 30%.
If we assume Staff and OPEX can substitute for each other then the scope for efficiency savings is 30% or so on each one of administrative staff and OPEX.
1999/00 2000/01 2001/02 2002/03 2003/04 2004/05
StaffModel
57.57 51.53 49.99 43.06 41.14 45.72
OPEXModel
72.44 71.2 69.73 72.59 74.57 75.1
JointModel
77.81 65.4 61.69 69.65 65.31 65.6
Efficiency Scores at a sample admin unit
Comparing the sample university with its benchmark units on Administrative Staff Costs
Data is indexed so that sample university of the previous slide = 1 on each variable.
Index PeerAdmin StaffCost
OPEXStudentIncome
NonAdminStaff
ResearchGrants
QR
2004/05
Benchmark A
0.47 0.67 1.57 1.19 0.42 0.11
Benchmark B
0.92 2.46 1.39 2.76 4.08 3.23
1999/00Benchmark B
1.00 2.51 1.46 2.35 3.99 3.28
Sector Findings on Efficiency
There are some 20 units with good benchmark performance without any scope for further efficiency savings. About half of these benchmark units are found to be consistently cost-efficient in all six years of our analysis. These units could prove examples of good operating practices in administration.
On the other hand some of the units with large scope for efficiency savings are so on all the six years suggesting persistent issues of expenditure control.
Visits to specific institutions did not support the notion that factors outside the model such as quality of service could explain differences in efficiency.
When we take administrative staff and OPEX as substitutable we find that the scope for efficiency savings is about 15% per annum in each.
TEACH/ £000
RES/ £000
A.
. B
.C
.D
*G
F .
2003/ 04 Data
2004/ 05 Data
2003/ 04 Boundary
.
*
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.
.
. .
H
E I
2004/ 05 Boundary
.
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* *
*
*
*
*
*
*
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5.0
//
OB
OF
OE
OG
OH
OF
OI
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]
Productivity is defined as the ratio of output to resource used.
TEACH/ £000
RES/ £000
A.
. B
.C
.D
*G
F .
2003/ 04 Data
2004/ 05 Data
2003/ 04 Boundary
.
*
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H
E I
2004/ 05 Boundary
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OI
OG
OB
OF /
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Efficiency catch up
OE
OIOB
OH X{
Boundary shift
Productivity change = Efficiency catch up x Boundary shift.
• }0.5
Bottom two HEIs on productivity
Data for 2004/5 – constant prices, Normalised so that 1999/00 = 1
Prod IndexAdmin
staff cost OPEXStudent income
Non Admin staff
Res’arch grants QR
0.7 1.93 0.98 1.23 0.9 1.23 0.81
0.74 1.41 1.42 1.04 0.98 1.05 10.8
In both universities the normalised data show substantial rise in admin staff costs against modest rise or even drop in activities.
Top three HEIs on productivity
Data for 2004/5 – constant prices, Normalised so that 1999/00 = 1
Prod IndexAdmin
staff cost OPEXStudent income
Non Admin staff
Res’arch grants QR
1.59 0.82 0.62 1.07 1.30 1.59 1.14
1.35 0.89 0.92 1.26 1.28 0.9 0.41
1.34 0.98 0.94 1.23 1.30 1.96 1.12
In these three universities that gain the most in admin productivity, admin costs fall over time while outputs rise, with only two exceptions on research income.
Productivity Change 1999/00 to 2004/5 – Staff Costs Model
NB: An index of 1 means stable productivity between 1999/0 and 2004/5.
An index below 1 means productivity drop. Eg. a value of 0.9 means the same work load is costing in 2004/5 11% more than it did in 1999/0. An index above 1 means productivity improvement.
ImprovingDeteriorating
Productivity Change Decomposition – Staff Model
Efficiency Catch-up Boundary Shift
Scale Efficiency Catch-up
Benchmark performance tends to deteriorate over time.
HEIs with negative effects due to scale exceed those with positive effects
HEIs tend to catch up with the boundary over time.
Productivity Change 1999/00 to 2004/5 – Staff and OPEX Combined
ImprovingDeteriorating
We have a virtually symmetrical distribution with half the units improving and the rest deteriorating in productivity.
Productivity Change Decomposition – Joint Model
Efficiency Catch-up Boundary Shift
Scale Efficiency Catch-up
There is clear evidence that the boundary is improving in that best performance is more productive in 2004/5 than in 1999/0. Most units are falling behind the boundary.
The catch-up and boundary shift results are the reverse from when staff costs were the sole input. This suggests perhaps that non staff expenses were managed better than staff costs, over time.
Scale efficiency deteriorates over time.
Summary of Findings on Productivity at Sector Level
Between 1999/00 and 2004/5 we find a divergent picture between administrative staff cost on the one hand and OPEX or the two inputs taken jointly on the other. In the case of administrative staff taken as the sole input we find that there is on average a drop in productivity so that for given levels of the proxy output variables staff cost is about 95% in 1999/00 compared to what it is in 2004/5, at constant prices.
Looking deeper it is found that generally units do keep up with the benchmark units but it is the benchmark units that are performing less productively by almost 7% in 2004/5 compared to 1999/00. The situation is not helped by a slight loss of productivity through scale sizes becoming less productive, by about 1.5% in 2004/5 compared to 1999/00.
In contrast when we look at OPEX as a sole input or indeed at administrative staff and OPEX as joint resources we find that productivity is more or less stable between 1999/00 and 2004/5. There is a slight loss of about 2% but given the noise in the data this is not significant.
What is significantly different between administrative staff on the one hand and OPEX or the two joint inputs on the other is that benchmark performance improves on average by about 8% between 1999/00 and 2004/5.
Unfortunately non benchmark units cannot quite keep up with this higher productivity. Also there is a slight deterioration again in scale size efficiency and the net effect is that despite the improved benchmark productivity, productivity on average is stable to slightly down between 1999/00 and 2004/5.
As with cost efficient practices here too our analysis has identified a small set of units which register significant productivity gains and others which register significant productivity losses between 1999/00 and 2004/5. An investigation of the causes in each case would be instrumental for offering advice to other units on how to gain in productivity over time and avoid losses.
Thank you…
