Modeling and Properties of Generalized Kanban Controlled

Assembly SystemsSbiti N.*, Di Mascolo M.**, Amghar M.*

FIFTH INTERNATIONAL CONFERENCEFIFTH INTERNATIONAL CONFERENCEANALYSIS OF MANUFACTURING SYSTEMS –ANALYSIS OF MANUFACTURING SYSTEMS –

PRODUCTION MANAGEMENTPRODUCTION MANAGEMENTMay 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

* LA2I **

Rabat - Morocco Grenoble - France

2

Studied systems

Make to stock pull controlled systems

Multistage production/inventory systems

Stage 1 Stage 2 Stage 3

demand

Manufacturing process Output buffer

raw parts finishedparts

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

3

Pull policies

Stage 1 Stage 2 Stage 3raw parts finished parts

demand

Local control : Kanban (~1960) (1 parameter : K)

Hybrid policies : Generalized Kanban [Buzacott 89] (K, S) Extended Kanban [Dallery, Liberopoulos 95]

Global control : Base-Stock (~1960) (1 parameter : S)

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

Parts flow : upstream downstream Information flow : downstream upstream

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

4

Assembly production systems

Stage 1

Stage 2

Stage 3

Raw parts 1

Raw parts 2

Finished parts

Kanban Base-Stock Generalized Kanban Extended Kanban

Serial stages

Assembly

ModelingAnalysis

ModelingAnalysis

ModelingAnalysis

ModelingAnalysis

Modeling

ModelingModelingAnalysis

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

5

Generalized Kanban :Serial stages

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

6

Generalized Kanban (serial stages)

Si = Ki KanbanKi = + Base-Stock

demand

MP3MP1 MP2

P1

A2

D2

B1

P2

A3

D3

B2

P3

A4

D4

B3K1 K2 K3

S1 S2 S3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

7

Assembly strategies:- simultaneous release

- independent release

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

8

Assembly strategies : principle

Assembly with simultaneous release Assembly with independent release

Stage 1

Stage 2

Stage 3K1 , S1

K2 , S2

K3 , S3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

9

Generalized Kanban assembly with Simultaneous release (GKS)

A4

P1

P2

A3

D3

B1

B2

P3

B3

D4

MP1

MP2

MP3

S1

S2

K1

K2

S3

K3

Stage 2

Stage 1

Stage 3

demand

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

10

Generalized Kanban assembly with Independent release (GKI)

P1

P2

A3A4

B1

D31

P3

B3

D4

MP1

MP2

MP3

D32

B2

demand

Stage 2

Stage 1

Stage 3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

S1

S2

K1

K2

S3

K3

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11

Properties

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

12

Invariance properties : GKS

Several closed sub-networks

K1

A4

P1

P2

A3

D3

B1

B2

P3

B3

D4

MP1

MP2

MP3

S1

S2 S3

K3

demandK2

K2

K3

K1

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

13

Invariance properties : GKS

Several closed sub-networks

K1

A4

P1

P2

A3

D3

B1

B2

P3

B3

D4

MP1

MP2

MP3

S1

S2 S3

K3

demandK2

S1 +K3S2 +K3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

14

Invariance properties : GKS

K1

A4

P1

P2

A3

D3

B1

B2

P3

B3

D4

MP1

MP2

MP3

S1

S2 S3

K3

demandK2

MP1 K1

MP2 K2

MP3 K3

P1 S1+K3P2 S2+K3

P3 S3

A3 K3D3 K3+min(S1, S2)

B1 K1

B2 K2

B3 K3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

15

Invariance properties : GKI

A4

P1

P2

A3

B1

D31

P3

B3

D4

MP1

MP2MP3

D32

B2

demand

D31 S1 + K3

D32 S2 + K3

Same boundsexcept that:

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

16

Time evolution ofGKS and GKI models

Relations between occurrence time of these events Evolution equations

For GKS and GKI models :

Stage 1

Stage 2

Stage 3O1,n

O2,n

O3,n

I1,n

I2,n

I3,n I4,n

1,n

2,n

3,n

Dn

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

17

Evolution equations of GKS models

Stage 1

Stage 2

Stage 3O1,n

O2,n

O3,n

I1,n

I2,n

I3,n I4,n

1,n

2,n

3,n

Dn

I1,n = max(Dn, O1,n-K1, O2,n-K2

, O3,n-

K3)

I2,n = I1,n

I3,n = max(Dn, O1,n-S1, O2,n-S2

, O3,n-

K3)

I4,n = max(Dn, O3,n-S3)

Oi,n = i,n+max(Ii,n, Oi,n-1)

for i=1,2,3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

18

Evolution equations of GKI models

Stage 1

Stage 2

Stage 3O1,n

O2,n

O3,n

I1,n

I2,n

I3,n I4,n

1,n

2,n

3,n

Dn

I1,n = max(Dn, O2,n-K2, O3,n-K3

)

I2,n = max(Dn, O1,n-K1, O3,n-K3

)

I3,n = max(Dn, O1,n-S1, O2,n-S2

, O3,n-

K3)

I4,n = max(Dn, O3,n-S3)

Oi,n = i,n+max(Ii,n, Oi,n-1)

for i=1,2,3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

19

Comparison of GKS and GKIsystems evolution

Response time of a GKI system Response time of a GKS system

Ii,nI Ii,nS i=1,2,3

Oi,nI Oi,n

S i=1,2,3

with DnI = Dn

S

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

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20

Influence of the parameters

For GKS and GKI systems :

Value of one parameter Response time

I’i,n Ii,n

i=1,2,3,4

O’i,n Oi,n i=1,2,3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

LA2I May 20-25, 2005 – Zakynthos Island, GreeceMay 20-25, 2005 – Zakynthos Island, Greece

21

Conclusion

Modeling of Generalized Kanban controlled assembly systems.

Special characteristics of Generalized Kanban not conserved.

GKI model generally faster than GKS model (response time).

Influence of parameters.

Performance evaluation

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