Data Envelopment Analysis

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DATA ENVELOPMENT ANALYSIS (DEA)
Steef van de Velde Rotterdam School of
Management Erasmus University
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DATA ENVELOPMENT ANALYSIS

• (QUITE CONTROVERSIAL) QUANTITATIVE TECHNIQUE FOR
  MEASURING
• THE RELATIVE EFFICIENCY (PERFORMANCE)
• OF
• RELATIVELY HOMOGENEOUS ORGANIZATIONAL UNITS
  .
• SUCH AS BANK BRANCHES, SCHOOLS, HOSPITALS,
  MUTUAL FUNDS, REHABILITATION CENTERS, RETAIL
  SHOPS, BUSINESS UNITS, OPERATING COMPANIES,
  AIRPORTS, LOCAL AUTHORITY DEPARTMENTS, COURTS OF
  JUSTICE .

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Plan of the Lecture

• Performance measurement - introduction
• DEA - the methodology
• DEA - interpretation of the results
• Modells Case

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CLOSING OF POLICE CELLS
CONSULTANCY PROJECT FOR THE ROTTERDAM POLICE
DEPARTMENT

• The Rotterdam police department has 10 precincts,
  each of which has a police station with police
  cells. Furthermore, there is one big police cell
  station at police headquarters
• Would it not be more efficient to centralize
  these cells? And have only 1 or 2 locations?
• After all, is a larger cell complex not more
  efficient than a smaller one (economies-of-scale)

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PERFORMANCE MEASUREMENTISCONTROVERSIA OR
EVEN EMOTIONALBUSINESS!!
DEA IS NO PANACEA
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DRINKING WATER INDUSTRY
BENCHMARKING A HOT EXAMPLE

• public utility sector
• 14 companies in the Netherlands
• voluntary benchmarking since 1997
• obligatory benchmarking since 2001 on
• 1. Quality
• 2. Customer service
• 3. Finance tariffs costs
• 4. Environment

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COST COMPARISON OF DRINKING WATER COMPANIES
Company Total Cubic Meters
Costs Supplied A 276130 68440 B
37442 15431 C 181307 63632 D 327352 98347 E 194
040 79826 F 113518 43522 G 62744 29752 H 2218
50 74266 I 151000 77093 J 200577 76894 K 123948
56402 L 221306 100230
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COST COMPARISON OF DRINKING WATER COMPANIES
Company Total Cubic Meter Number
of Costs Supplied
Households A 276130 68440 530 B
37442 15431 97 C 181307 63632 413 D 327352 9
8347 664 E 194040 79826 490 F 113518 43522 26
9 G 62744 29752 184 H 221850 74266 450 I 15
1000 77093 400 J 200577 76894 481 K 123948 564
02 313 L 221306 100230 566
SURE, MY COSTS ARE (RELATIVELY) HIGH!! AFTER
ALL, MY CUSTOMER SERVICE ANDMY QUALITY ARE
EXCEPTIONALLY GOOD.
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COST COMPARISON OF DRINKING WATER COMPANIES
Company Total Cubic Meter Number
of Costs Supplied
Households A 276130 68440 530 B
37442 15431 97 C 181307 63632 413 D 327352 9
8347 664 E 194040 79826 490 F 113518 43522 26
9 G 62744 29752 184 H 221850 74266 450 I 15
1000 77093 400 J 200577 76894 481 K 123948 564
02 313 L 221306 100230 566
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COST COMPARISON OF DRINKING WATER COMPANIES
Company Total Cubic Meter Number
of Costs Supplied
Households A 276130 68440 530 B
37442 15431 97 C 181307 63632 413 D 327352 9
8347 664 E 194040 79826 490 F 113518 43522 26
9 G 62744 29752 184 H 221850 74266 450 I 15
1000 77093 400 J 200577 76894 481 K 123948 564
02 313 L 221306 100230 566
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COMMON COMPLAINTS

• YOURE MEASURING THE WRONG THINGS
• YOU ARE WEIGHING THE PERFORMANCE MEASURES
  INCORRECTLY (I FIND THIS ASPECT MORE IMPORTANT
  THAN YOU DO)

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LETS INTRODUCE SOME SYSTEMATIC THINKING!!
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SINGLE INPUT AND SINGLE OUTPUT
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BASIC (AND WIDELY ACCEPTED) ASSUMPTION ...
OUTPUT
EFFICIENCY
INPUT
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MANY OTHER EXAMPLES

• IMPACT FACTORS OF SCIENTIFIC JOURNALS
• cited papers/published papers
• GPA STUDENT RANKING
• RETURN ON INVESTMENT
• BATTING AVERAGE (IN BASEBALL)
• MUTUAL FUNDS (SHARP RATIO)

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Efficient Frontier
6 5 4 3 2 1 0
SALES
B
AVERAGEPERFORMANCE (OBTAINED BY
REGRESSION ANALYSIS)
A
0 1 2 3 4 5
6 7 8 9
EMPLOYEE
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TWO INPUTS , ONE OUTPUT CASE
LETS NORMALIZE SALES!!!
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AREA
6 5 4 3 2 1 0
G
E
A
B
H
I
F
Efficient Frontier
D
C
0 1 2 3 4 5
6 7 8 9
EMPLOYEE
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MULTIPLE INPUTS MULTIPLE OUTPUTS
HOWEVER, VERY OFTEN .

• DIFFERENT RESOURCES
• DIFFERENT ACTIVITIES

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2003 FINANCIAL TIMESEMBA RANKING
PAINFUL EXAMPLE...

• 14. PURDUE/TIAS
• 48. SMURFIT (DUBLIN)
• 50. RSM (down from 26)

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IN GENERAL
EFFICIENCY
WEIGHTED SUM OF OUTPUTS
WEIGHTED SUM OF INPUTS
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Weight doctor 5 Weight nurses 1 Weight
outpatient 1 Weight inpatient 3
TWO INPUTS , TWO OUTPUTS CASE
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HOW TO DETERMINE SUCH A COMMON WEIGHTS?

• CONSENSUS?
• RULE OF THUMB?
• TOP DOWN?

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MULTIPLE INPUTS MULTIPLE OUTPUTS
FURTHERMORE .

• DIFFERENT RESOURCES
• DIFFERENT ACTIVITIES
• ENVIRONMENTAL FACTORS

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DATA ENVELOPMENT ANALYSIS

• HANDLES MULTIPLE INPUT AND OUTPUT FACTORS
• CAN HANDLE ENVIRONMENTAL FACTORS
• DOES NOT REQUIRE A SPECIFICATION OF A FUNCTIONAL
  FORM OF INPUT-OUTPUT CORRESPONDENCE
• GIVES NONETHELESS A SINGLE MEASURE OF PERFORMANCE

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CHARNES, COOPER RHODES (1978)
BREAKTHROUGH IDEA

• WEIGHTED SUM OF OUTPUTS
• EFFICIENCY
• WEIGHTED SUM OF INPUTS
• FOR EACH UNIT, DO THE FOLLOWING
• CHOOSE THE BEST SET OF (POSITIVE) WEIGHTS (SO NO
  COMMON SET OF WEIGHTS) SO AS TO MAXIMIZE ITS
  EFFICIENCY
• AND SUCH THAT
• THE EFFICIENCY OF ALL THE UNITS ? 1
• (EXPRESSED IN THOSE WEIGHTS)

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TWO INPUTS , TWO OUTPUTS CASE DEA EFFICIENCY
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HYPOTHETICAL CASE DISTRIBUTOR OF
PHARMACEUTICALS
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EFFICIENCY OFDEPOT 1
1
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EFFICIENCY OFDEPOT 1
1
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EFFICIENCY OFDEPOT 1
1
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EFFICIENCY OFDEPOT 1
1
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EFFICIENCY OFDEPOT 1
1
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RESULTS FOR DEPOT 1

• Efficiency depot 1 0.82
• Weights (suppose)
• u1 0.60 u2 0.12 u3 0.36
• v1 0.45 v2 0.18
• Other efficiencies
• depot 2 0.83
• depot 3 0.75
• ...
• depot 15 1.00
• ...

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WHY IS DEPOT 1s EFFICIENCY NOT EQUAL TO 1.00?

• Consider the following situation
• Raf Steef
• Management Science 7 8
• Information Systems 6 7
• No matter the weights, Rafs efficiency is always
  smaller than Steefs.

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EFFICIENCY OFDEPOT 2
?
?
?
2
?
?
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EFFICIENCY OFDEPOT 2
45
50
40
2
2.5
4.5
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NOTE ...

• only the objective function differs
• most likely, the set of best weights for depot 2
  differs from the set of best weights for depot 1

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RESULTS FOR DEPOT 2

• Efficiency depot 2 0.94
• Weights (suppose)
• u1 0.42 u2 0.23 u3 0.02
• v1 0.26 v2 0.44
• Other efficiencies
• depot 1 0.63
• depot 3 0.45
• ...
• depot 12 1.00
• ...

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Each model can be transformed into a linear
programming model!!!

• With regard to the constraints
• Each constraint is of the type y/x lt 1.
• This is equivalent to y lt x,
• and hence y - x lt 0 (which is linear)

• With regard to the objective function (of the
  type max a/b)
• The weights are relative,
• and hence we can normalize the denominator
  simply by letting b 100 (for instance) and
  rewrite the objective function as
• max a subject to b 100 and subject to the
  other constraints

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FREEWARE DEA SOFTWAREAVAILABLE

• (FOR ACADEMIC USE ONLY)
• SEE BLACKBOARD
• NOT REALLY USER-FRIENDLY -(

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TWO POSSIBLE TYPES OF OUTCOMES

• THE EFFICIENCY OF DEPOT 1 EQUALS 1.0
• THE EFFICIENCY OF DEPOT 1 lt 1.0 ..

WHAT DO THEY MEAN/SUGGEST?
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FLEXIBILITY IN THE CHOICE OF WEIGHTS

• IS A WEAKNESS .. (WHEN EFFICIENCY 1.0)
• WHY?
• MANY UNITS MAY BE EFFICIENT, ONLY BY A SMART
  CHOICE OF THE WEIGHTS.
• YOU MEASURE ONLY RELATIVE PERFORMANCE
• INDEED WITH t OUTPUTS AND m INPUTS, WE MAY HAVE
  t x m EFFICIENT UNITS

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AREA
IS UNIT J EFFICIENT?
6 5 4 3 2 1 0
NO!!! UNIT J HAS EXCESSIN INPUT (EMPLOYEES)!!!
G
E
A
B
H
I
F
Efficient Frontier
D
J
C
0 1 2 3 4 5
6 7 8 9
EMPLOYEE
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A UNIT IS EFFICIENT ONLY IF

• Efficiency 1.0, and
• v gt 0 and u gt 0 !!!!!

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FLEXIBILITY IN THE CHOICE OF WEIGHTS ...

• IS A STRENGTH .. (WHEN EFFICIENCY lt 1.0)
• WHY?

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BROADLY SPEAKING DEPOT 18 SHOULD HAVE BEEN ABLE
TO SUPPORT ITS ACTIVITY LEVELS WITH ONLY 42 of
ITS RESOURCES
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FURTHERMORE .

• FOR AN INEFFICIENT UNIT, AT LEAST ONE OTHER
  UNIT WILL BE EFFICIENT WITH THETARGET UNITS
  SET OF WEIGHTS!
• THE SO-CALLED PEER GROUP FOR THE INEFFICIENT
  UNIT

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FURTHERMORE .

• FOR AN INEFFICIENT UNIT, THE LINEAR
  PROGRAMMING SOLUTION WILL PROVIDE A SET OF TARGET
  INPUTS AND OUTPUTS.

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INCORPORATING ENVIRONMENTAL FACTORS
NON-DISCRETIONARY VARIABLES

• the number of parents with university degrees for
  computing the efficiency of high schools
• Competition, demographics (retail shops)

CAN BE CONSIDERED AS ADDITIONAL RESOURCES!!!
CAN BE CONSIDERED AS ADDITIONAL OUTPUTS
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EXAMPLES

• C1000 (DUTCH SUPERMARKET CHAIN)
• DUTCH COURTS OF JUSTICE
• MBA SCHOOLS .
• PUBLIC UTILITY COMPANIES
• GAS STATIONS (BP SHELL)
• DISTRIBUTION DROP-OFF POINTS FOR MAGAZINES AND
  JOURNALS

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CLOSING OF POLICE CELLS
CONSULTANCY PROJECT FOR THE ROTTERDAM POLICE
DEPARTMENT

• The Rotterdam police department has 10 precincts,
  each of which has a police station with police
  cells. Furthermore, there is one big police cell
  station at police headquarters
• Would it not be more efficient to centralize
  these cells? And have only 1 or 2 locations?
• After all, is a larger cell complex not more
  efficient than a smaller one (economies-of-scale)

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DEA MODEL?
Number of cell days
POLICE STATION
Number of detainees
number of person shifts
Number of vav detainees
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DEA-Analyse
central
central
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REACTIONS?

• USEFUL TECHNIQUE?
• DO YOU BELIEVE IN IT?
• HOW WOULD YOU APPLY IT IN PRACTICE?
• WHICH ADDITIONAL APPLICATIONS CAN YOU THINK OF?

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CONCLUSION

• DEA IS AN INTERESTING AND POWERFUL TOOL FOR
  BENCHMARKING
• NOT A PANACEA ALSO SHORTCOMINGS
• measures RELATIVE performance, not ABSOLUTE
  performance
• also the inputs and outputs are still up for
  debate
• WORKS PROBABLY BEST IN COMBINATION WITH OTHER,
  COMPLIMENTARY METHODS