Data Envelopment Analysis (DEA)
Identifying Efficient Decision Making Units
Measuring Service Productivity
Branch Bank Example
1. ACCOUNTING RATIO: COST PER TELLER TRANSACTION
HIGHER RATIO WOULD BE INEFFICIENT RELATIVE TO OTHERS, BUT COULD BE
EXPLAINED BY:
1. MIX OF OUTPUTS (SELLING CD’S VS SIMPLE DEPOSITS)
2. MIX OF INPUTS (USE OF ATM’S AND LIVE TELLERS)
2. BROAD BASED MEASURE: RETURN ON INVESTMENT
OVERALL IMPORTANT BUT NOT SUFFICIENT TO EVALUATE OPERATING EFFICIENCY
OF INDIVIDUAL DECISION MAKING UNIT (DMU)
FOR EXAMPLE:
A PROFITABLE BRANCH COULD BE THE RESULT OF HIGHER-THAN-AVERAGE
PROPORTION OF REVENUE GENERATING TRANSACTIONS RATHER THAN
COST-EFFICIENT USE OF RESOURCES.
THE DEA MODEL
Fractional Form
Objective Function
max Ee 
u1O1e  u2 O2 e    u M OMe
v1 I1e  v2 I 2 e    v N I Ne
Constraints
u1O1k  u2 O2 k    u M OMk
 10
.
v1 I1k  v2 I 2 k    v N I Nk
j  0
i  0
j =1,2,…,M
i= 1,2,…,N
k  1, 2, , K
DEA in Standard LP Form
(Scaling inputs to sum to 1.0)
STANDARD LP FORM(scaling inputs to sum of 1.0)
max E e  u1O1e  u2 O2 e      u M O Me
SUBJECT TO:
v1 I 1e  v2 I 2 e     v N I Ne  1
u1O1k  u2 O2 k    u M O Mk   v1 I 1k  v2 I 2 k    v N I Nk   0
where:
uj  0
j  1, 2 ,    , M
vi  0
i  1, 2 ,    , N
K  2 N  M 
RECOMMENDED SAMPLE SIZE:
k  1, 2, , K
Burger Palace Example
SUMMARY OF OUTPUTS AND INPUTS FOR BURGER PALACE
Service unit
1
2
3
4
5
6
Meals sold
100
100
100
100
100
100
Labor-hours
2
4
4
6
8
10
Material dollars
200
150
100
100
80
50
LP MODEL FOR EVALUATION OF SERVICE UNIT 1
max E ( S1 )  u1100
subject to:
u1100  v1 2  v2 200  0
u1100  v1 4  v2 150  0
u1100  v1 4  v2 100  0
u1100  v1 6  v2 100  0
u1100  v1 8  v2 80  0
u1100  v110  v2 50  0
v1 2  v2 200  1
u1 , v1 , v2  0
Burger Palace
Productivity Frontier
Material dollars
200
S1 (2,200)
150
S2 (4,150)
100
S3 (4,100)
S4 (6,100)
S5 (8,80)
C (5.3, 88.9)
50
S6 (10,50)
0
0
2
4
6
Labor hours
8
10
Summary of DEA Results
SUMMARY OF DEA RESULTS
Service unit
Efficiency
rating (E)
Efficiency
reference set
Relative labor-hour
value  v1 
Relative material
value v2 
S1
S2
1.000
0.857
.1667
.1428
.0033
.0028
S3
S4
1.000
0.889
.0625
.0555
.0075
.0067
S5
0.901
.0568
.0068
S6
1.000
N.A.
S1 (.2857)
S3 (.7143)
N.A.
S3 (.7778)
S6 (.2222)
S3 (.4545)
S6 (.5454)
N.A.
.0625
.0075
CALCULATION OF EXCES INPUTS USED BY UNIT S4
Outputs and
inputs
Meals
Labor-hours
Material $
Reference set
S3
(.7778)
(.7778)
(.7778)
×
×
×
100
4
100
+
+
+
(.2222)
(.2222)
(.2222)
Composite
reference
unit C
S6
×
×
×
100
10
50
=
=
=
100
5.3
88.9
S4
100
6
100
Excess
inputs used
0
0.7
11.1
DEA and Strategic Planning
High
Profit
Low
Under-performing
potential stars
Benchmark
group
Problem
Branches
Candidates
for divestiture
Low
High
Efficiency