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