GOOD

1. Data Envelopment Analysis (DEA)
Identifying Efficient Decision Making Units

2. 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.

3. THE DEA MODEL
Fractional Form
Objective Function
max E
u O u O u O
v I v I v I
e
e e M Me
e e N Ne

  
  
1 1 2 2
1 1 2 2


Constraints
u O u O u O
v I v I v I
k K
k k M Mk
k k N Nk
1 1 2 2
1 1 2 2
10 1 2
  
  
 



. , , ,


j
i


0
0
j =1,2,…,M
i= 1,2,…,N

4. DEA in Standard LP Form
(Scaling inputs to sum to 1.0)
STANDARD LP FORM(scaling inputs to sum of 1.0)
max E u O u O u O
e e e M Me
   
1 1 2 2
SUBJECT TO:
v I v I v I
e e N Ne
1 1 2 2 1
   
 
u O u O u O v I v I v I k K
k k M Mk k k N Nk
1 1 2 2 1 1 2 2 0 1 2
        
  
, , ,
where:
u j M
v i N
j
i
  
  
0 1 2
0 1 2
, , ,
, , ,
RECOMMENDED SAMPLE SIZE:  
K N M
 
2

5. Burger Palace Example
SUMMARY OF OUTPUTS AND INPUTS FOR BURGER PALACE
Service unit Meals sold Labor-hours Material dollars
1 100 2 200
2 100 4 150
3 100 4 100
4 100 6 100
5 100 8 80
6 100 10 50
LP MODEL FOR EVALUATION OF SERVICE UNIT 1
max ( )
E S u
1 1100

subject to:
u v v
u v v
u v v
1 1 2
1 1 2
1 1 2
100 2 200 0
100 4 150 0
100 4 100 0
  
  
  
u v v
u v v
u v v
v v
u v v
1 1 2
1 1 2
1 1 2
1 2
1 1 2
100 6 100 0
100 8 80 0
100 10 50 0
2 200 1
0
  
  
  
 

, ,

6. Burger Palace
Productivity Frontier
0
50
100
150
200
0 2 4 6 8 10
Labor hours
Material
dollars
S1 (2,200)
S2 (4,150)
S3 (4,100) S4 (6,100)
S5 (8,80)
S6 (10,50)
C (5.3, 88.9)

7. 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 1.000 N.A. .1667 .0033
S2 0.857 S1 (.2857)
S3 (.7143)
.1428 .0028
S3 1.000 N.A. .0625 .0075
S4 0.889 S3 (.7778)
S6 (.2222)
.0555 .0067
S5 0.901 S3 (.4545)
S6 (.5454)
.0568 .0068
S6 1.000 N.A. .0625 .0075
CALCULATION OF EXCES INPUTS USED BY UNIT S4
Outputs and
inputs Reference set
Composite
reference
unit C
Excess
inputs used
S3 S6 S4
Meals (.7778) × 100 + (.2222) × 100 = 100 100 0
Labor-hours (.7778) × 4 + (.2222) × 10 = 5.3 6 0.7
Material $ (.7778) × 100 + (.2222) × 50 = 88.9 100 11.1

8. DEA and Strategic Planning
Under-performing Benchmark
potential stars group
Problem Candidates
Branches for divestiture
High
Low
Profit
Low High
Efficiency