Transcript MEASURING SERVICE PRODUCTIVITY
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
E e
u O
1 1
e v I
1 1
e
u O
2 2
v I
2 2
e e u O M Me v I N Ne
Constraints
u O
1 1
k v I
1 1
k
u O
2
v I
2 2 2
k k
j
i
0 0
u O M Mk v I N Nk
j =1,2,…,M i= 1,2,…,N k
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
1
e
u O
2
e
u M O Me
SUBJECT TO:
v I
1
e
2
e
Ne
1 1
k
u O
2
k
u M O Mk
where:
u j v i
0 0
j
i
,
M
,
N
1
k
2
k
K
2
N
M
Nk
0
k
RECOMMENDED SAMPLE SIZE: ,
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 S
1 )
u
1 100 subject to:
u
1 100
u
1 100
u
1 100
u
1 100
u
1 100
u
1 100
v v
1 2
v
1 4
v
1 4
v
1 6
v
1 8 1 10
v
2 200
v v v
2 2 2
v v
150 100 100 2 2 80 50
v
1 2
v
2 200 0 0 0 0 0 0 1 , 1 ,
v
2 0
200 150 100 50 0 0
Burger Palace Productivity Frontier
S1 (2,200) S2 (4,150) S3 (4,100) S4 (6,100) S5 (8,80) C (5.3, 88.9) S6 (10,50) 2 4 6
Labor hours
8 10
Summary of DEA Results
SUMMARY OF DEA RESULTS Service unit
S
1
S
2
S
3
S
4
S
5
S
6
Efficiency rating (E)
1.000
0.857
1.000
0.889
0.901
1.000
Efficiency reference set
S
1
S
3
S
3
S
6
S
3
S
6 N.A.
(.2857) (.7143) N.A.
(.7778) (.2222) (.4545) (.5454) N.A.
Relative labor-hour value
.1667
.1428
Relative material
.0033
.0028
.0625
.0555
.0075
.0067
.0568
.0625
.0068
.0075
CALCULATION OF EXCES INPUTS USED BY UNIT S4 Outputs and inputs
Meals Labor-hours Material $ (.7778) × (.7778) × (.7778) ×
Reference set
S
3 100 + 4 + 100 + (.2222) × (.2222) × (.2222) ×
S
6 100 = 10 = 50 =
Composite reference unit C
S
4 100 5.3
88.9
100 6 100
Excess inputs used
0 0.7
11.1
DEA and Strategic Planning
High Under-performing Benchmark potential stars group
Profit
Low Problem Candidates Branches for divestiture Low
Efficiency
High