CIE39 Troyes

CIE39, Troyes,July 6, 2009

Using Data Envelopment Analysis to benchmark logistic performance

in Belgian manufacturing companies

Sofie Van Volsem, Hendrik Van LandeghemDepartment of Industrial Management, Ghent University, Belgium

([email protected])

CIE39, Troyes,July 6, 2009CIE39, Troyes,July 6, 2009

Aggregate information

Multi-Input Multi-Output

DEA

•Efficient Frontier

•Efficient Input and

Output target

Extending classical Output / Input rate

Hypothesis: Input/Output relationship is assumed

2


Identification Best-Practice Frontier

0

1

2

3

4

5

0 1 2 3 4 5

Input

Ou

tpu

t

D

B

C

A

S. Van Volsem 3

INEFFICIENT

DMU name Input OutputA 1 1B 2 3C 4 4D 3 2


Type of Frontier

0

1

2

3

4

5

0 1 2 3 4 5 6

input

ou

tpu

t

B

C

A

D

•VRS: Variable Return to Scale.

Removing the constraint

With the constraint:

∑λj = 1


∑λj ≤ 1


∑λj ≥ 1

•NDRS: Non-Decreasing Return to Scale.•CRS: Constant Return to Scale.•NIRS: Non-Increasing Return to Scale.•VRS: Variable Return to Scale

•CRS: Constant Return to Scale

•NIRS: Non-Increasing Return to Scale

•NDRS: Non-Decreasing Return to Scale

n

1jjλ

CIE39, Troyes, 6-8 July 2009

4S. Van Volsem


0

1

2

3

4

5

0 1 2 3 4 5

Input

Ou

tpu

t

D

B

C

A

•Input-oriented approach

•Output-oriented approach

Two alternative approaches

1,5

D’

0,53

1,5

InputPresent

InputEfficientθ

D’3,5

1,752

3,5

OutputPresent

OutputEfficient

5



n,...,2,1j0

1

s,...,2,1rysy

m,...,2,1ixsx

tosubject

)ss(min

j

n

1jj

n

1j0rrrjj

n

1j0iiijj

m

1i

s

1rri

n,...,2,1j0

1

s,...,2,1rysy

m,...,2,1ixsx

tosubject

)ss(max

j

n

1jj

n

1j0rrrjj

n

1j0iiijj

m

1i

s

1rri

VRS Envelopment ModelInput-Oriented Output-Oriented

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0

1

2

3

4

5

0 1 2 3 4 5 6

Input

Ou

tpu

tE

B

C

A

D

Slacks

7S. Van Volsem


Undesirable Measures Model

Undesirable Outputs may be present: outputs we wish to decrease

Internal processes and

activities

% BP LEAN

% BP INV

% BP CIM

% BP LOGPLAN

% Perfect Orders

Days of Inventory

Flexibility

8S. Van Volsem


Days needed to increase productivity by 20%


Undesirable Measures Model

Output-Oriented Model with Undesirables Measures: and

0vyy rbrj

brj 1ymaxv b

rjjr

grjy b

rjy

n,...,2,1j;0

1

xx

yy

yhy

tosubject

hmax

j

n

1jj

n

1j0iijj

n

1j

b0r

brjj

n

1j

g0r

grjj

*r

b0r

*r

b0r

*r

g0r

*g0r

*i0i0i

syhvy

syhy

sxx

where

Efficient target for DMU0

9



DEA Models in Spreadsheets

Joe Zhu

“Quantitative Models for Performance Evaluation and Benchmarking”

2003

Excel Spreadsheets

Solver

Visual Basic+

10S. Van Volsem



Benchmarking applied on logistics Case 80 Belgium companies

Best Practices Data

General Best Practice rate

Human Resources, Assets, Design, quality control,

Inventory,…

Best Practices related with logistics

• Logistic plan (LOGPLAN)

• Inventory (INV)

• Lean (LEAN)

• Monitorizaton (CIM)

11S. Van Volsem



General BP adoption



activities

% BP LEAN

% BP INV

% BP CIM

% BP LOGPLAN

ROA

Cash Cycle Time

Added Value

TEST 1: Multi-input / Multi-output – general output

% BP LEAN

% BP INV

% BP CIM

% BP LOGPLAN

TEST 2: Multi-input / Multi-output – logistics output

TESTS

% Perfect Orders

Days of Inventory

Flexibility


activities

13S. Van Volsem




activities

% BP LEAN

% BP INV

% BP CIM

% BP LOGPLAN

Results Test 1 : general output

Results:

Efficiency

Frequency

1,61,51,41,31,21,11,0

10

9

8

7

6

5

4

3

2

1

0

1

0

11

2

4

10

Histogram of Efficiency

DMU No.

Output-OrientedEfficiency

1 1,370782 1,191804 1,105726 1,5860010 1,0963611 1,3331912 1,0783114 1,1897419 1,06008

ROA

Cash Cycle Time

Added Value

14



% BP LEAN

% BP INV

% BP CIM

% BP LOGPLAN

Efficiency

Frequency

1,161,121,081,041,00

1817161514131211109876543210

1000000

10

17

Histogram of Efficiency

DMU No.

Output-OrientedEfficiency

2 1,002045 1,0019911 1,0421114 1,18687

% Perfect Orders

Days of Inventory

Flexibility

Results Test 2 : logistics output

Results:


activities

15



What can we offer to companies?

• A benchmarking tool

• Identification of Efficient Frontier

• Relative efficiency in the set of companies

• Visual information

For this, we only need aggregate data => low information cost

16S. Van Volsem


Efficient company

52,2 % BPCIM

52,9 % BPINV

36,4 % BPLEAN

28,6 % BPLOGPLAN

COMPANY ID_DAT_TIM:

720304081839

96 days Inv.

• Company Position: 1/19

18 days Prod.

94% P. O.

Efficient

Visual information display

17S. Van Volsem


Non-efficient company

47,8 % BPCIM

64,7 % BPINV

27,3 % BPLEAN

39,3% BPLOGPLAN

COMPANY ID_DAT_TIM:

3130501241053

40 days Inv. 17 days

80 days Prod. 3 days

50% P. O. 77,5 %

96%

58%

55%

COMPANY POSITION:

19/19


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Relative position in the whole set

0%

10%

20%

30%

40%

50%

Po

ssib

le i

mp

rove

me

nt

23 CompaniesEFFICIENT

YOUR COMPANY

20 / 23

33 %


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Conclusions: Data Envelopment Analysis as a benchmarking tool

• Identification of efficient companies and output efficient targets

• No information about how to improve internal performance to reach the efficiency

• Relationship Input-Output is assumed

• Quality of a DEA benchmarking does highly depend on the available data

• Visual information display available20S. Van Volsem

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