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