Modeling and Properties of Generalized Kanban Controlled Assembly Systems

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

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

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

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

Modeling

ModelingModelingAnalysis

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

Generalized Kanban :Serial stages

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

Generalized Kanban (serial stages)

Si = Ki KanbanKi = + Base-Stock

demand

MP3MP1 MP2

B3K1 K2 K3

S1 S2 S3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

Assembly strategies:- simultaneous release

- independent release

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

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

Generalized Kanban assembly with Simultaneous release (GKS)

Stage 2

Stage 1

Stage 3

demand

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

Generalized Kanban assembly with Independent release (GKI)

demand

Stage 2

Stage 1

Stage 3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

Properties

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

Invariance properties : GKS

Several closed sub-networks

demandK2

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

Several closed sub-networks

demandK2

S1 +K3S2 +K3

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

demandK2

MP1 K1

MP2 K2

MP3 K3

P1 S1+K3P2 S2+K3

A3 K3D3 K3+min(S1, S2)

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

Invariance properties : GKI

MP2MP3

demand

D31 S1 + K3

D32 S2 + K3

Same boundsexcept that:

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

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

I3,n I4,n

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

Evolution equations of GKS models

Stage 1

Stage 2

Stage 3O1,n

I3,n I4,n

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

, O3,n-

I2,n = I1,n

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

, O3,n-

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

Evolution equations of GKI models

Stage 1

Stage 2

Stage 3O1,n

I3,n I4,n

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

, O3,n-

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

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

Introduction

Generalized Kanban

Assembly strategies

Properties

Conclusion

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

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

Modeling and Properties of Generalized Kanban Controlled Assembly Systems

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Transcript of Modeling and Properties of Generalized Kanban Controlled Assembly Systems

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