Dea analysis
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Transcript of Dea analysis
Data Envelopment Analysis (DEA)
Identifying Efficient Decision Making Units
Measuring Service ProductivityBranch 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 MODELFractional Form
O b j e c t i v e F u n c t i o n
m a x Eu O u O u O
v I v I v Iee e M M e
e e N N e
1 1 2 2
1 1 2 2
C o n s t r a i n t s
u O u O u O
v I v I v Ik Kk k M M k
k k N N k
1 1 2 2
1 1 2 2
1 0 1 2
. , , ,
j
i
0
0
j =1,2,…,M
i= 1,2,…,N
DEA in Standard LP Form (Scaling inputs to sum to 1.0)
S T A N D A R D L P F O R M ( s c a l i n g i n p u t s t o s u m o f 1 . 0 )
m a x E u O u O u Oe e e M M e 1 1 2 2
S U B J E C T T O :
v I v I v Ie e N N e1 1 2 2 1
u O u O u O v I v I v I k Kk k M M k k k N N k1 1 2 2 1 1 2 2 0 1 2 , , ,
w h e r e :
u j M
v i Nj
i
0 1 2
0 1 2
, , ,
, , ,
R E C O M M E N D E D S A M P L E S I Z E : K N M 2
Burger Palace Example
S U M M A R Y O F O U T P U T S A N D I N P U T S F O R B U R G E R P A L A C E
S e r v ic e u n i t M e a ls s o ld L a b o r - h o u r s M a t e r ia l d o l la r s 1 1 0 0 2 2 0 0 2 1 0 0 4 1 5 0 3 1 0 0 4 1 0 0 4 1 0 0 6 1 0 0 5 1 0 0 8 8 0 6 1 0 0 1 0 5 0
L P M O D E L F O R E V A L U A T I O N O F S E R V I C E U N I T 1
m a x ( )E S u1 1 1 0 0
s u b je c t to :
u v v
u v v
u v v
1 1 2
1 1 2
1 1 2
1 0 0 2 2 0 0 0
1 0 0 4 1 5 0 0
1 0 0 4 1 0 0 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
1 0 0 6 1 0 0 0
1 0 0 8 8 0 0
1 0 0 1 0 5 0 0
2 2 0 0 1
0
, ,
Burger Palace Productivity Frontier
0
50
100
150
200
0 2 4 6 8 10
Labor hours
Mat
eria
l dol
lars
S1 (2,200)
S2 (4,150)
S3 (4,100) S4 (6,100)
S5 (8,80)
S6 (10,50)C (5.3, 88.9)
Summary of DEA Results
SUMMARY OF DEA RESULTS
Service unitEfficiencyrating (E)
Efficiencyreference set
Relative labor-hourvalue v1
Relative materialvalue v2
S1 1.000 N.A. .1667 .0033S2 0.857 S1 (.2857)
S3 (.7143).1428 .0028
S3 1.000 N.A. .0625 .0075S4 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 andinputs Reference set
Compositereference
unit CExcess
inputs used
S3 S6 S4
Meals (.7778) × 100 + (.2222) × 100 = 100 100 0Labor-hours (.7778) × 4 + (.2222) × 10 = 5.3 6 0.7Material $ (.7778) × 100 + (.2222) × 50 = 88.9 100 11.1
DEA and Strategic Planning
Under-performing Benchmark potential stars group
Problem Candidates Branches for divestiture
High
Low
Profit
Low High Efficiency