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Modeling and Properties of Generalized Kanban Controlled Assembly Systems

* LA2I. **. Modeling and Properties of Generalized Kanban Controlled Assembly Systems. FIFTH INTERNATIONAL CONFERENCE ANALYSIS OF MANUFACTURING SYSTEMS – PRODUCTION MANAGEMENT May 20-25, 2005 – Zakynthos Island, Greece. Sbiti N.*, Di Mascolo M.**, Amghar M.*. Rabat - Morocco.

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Modeling and Properties of Generalized Kanban Controlled Assembly Systems

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  1. * LA2I ** Modeling and Properties of Generalized Kanban Controlled Assembly Systems FIFTH INTERNATIONAL CONFERENCE ANALYSIS OF MANUFACTURING SYSTEMS – PRODUCTION MANAGEMENT May 20-25, 2005 – Zakynthos Island, Greece Sbiti N.*, Di Mascolo M.**, Amghar M.* Rabat - Morocco Grenoble - France

  2. May 20-25, 2005 – Zakynthos Island, Greece LA2I Manufacturing process Output buffer Introduction Generalized Kanban Assembly strategies Properties Conclusion Studied systems  Make to stock pull controlled systems  Multistage production/inventory systems demand  finished parts raw parts Stage 1 Stage 2 Stage 3

  3. May 20-25, 2005 – Zakynthos Island, Greece LA2I Parts flow : upstream downstream Information flow : downstream upstream Introduction Generalized Kanban Assembly strategies Properties Conclusion Pull policies demand raw parts finished parts Stage 1 Stage 2 Stage 3 Local control : Kanban (~1960) (1 parameter : K) Global control : Base-Stock (~1960) (1 parameter : S) Hybrid policies :Generalized Kanban [Buzacott 89] (K, S) Extended Kanban[Dallery, Liberopoulos 95]

  4. May 20-25, 2005 – Zakynthos Island, Greece LA2I Base-Stock Kanban Extended Kanban Generalized Kanban Modeling Analysis Modeling Analysis Modeling Analysis Modeling Serial stages Modeling Analysis Modeling Assembly Modeling Analysis Introduction Generalized Kanban Assembly strategies Properties Conclusion Assembly production systems Stage 1 Raw parts 1 Stage 3 Finished parts Stage 2 Raw parts 2

  5. May 20-25, 2005 – Zakynthos Island, Greece LA2I Introduction Generalized Kanban Assembly strategies Properties Conclusion Generalized Kanban :Serial stages

  6. May 20-25, 2005 – Zakynthos Island, Greece LA2I Si = Ki Kanban Ki = + Base-Stock Introduction Generalized Kanban Assembly strategies Properties Conclusion Generalized Kanban (serial stages) S1 S2 S3 P1 P2 P3 A2 A3 A4 MP1 MP2 MP3 D2 D3 D4 B1 B2 B3 K1 K2 K3 demand

  7. May 20-25, 2005 – Zakynthos Island, Greece LA2I Introduction Generalized Kanban Assembly strategies Properties Conclusion Assembly strategies: - simultaneous release - independent release

  8. May 20-25, 2005 – Zakynthos Island, Greece LA2I Introduction Generalized Kanban Assembly strategies Properties Conclusion Assembly strategies : principle  Assembly with simultaneous release  Assembly with independent release Stage 1 Stage 3 K1 , S1 Stage 2 K3 , S3 K2 , S2

  9. May 20-25, 2005 – Zakynthos Island, Greece LA2I Stage 1 Stage 3 Stage 2 Introduction Generalized Kanban Assembly strategies Properties Conclusion Generalized Kanban assembly with Simultaneous release (GKS) P1 S1 P2 MP1 P3 S2 S3 A3 A4 MP3 D3 MP2 D4 B1 B3 K1 B2 K3 K2 demand

  10. May 20-25, 2005 – Zakynthos Island, Greece LA2I Stage 1 Stage 3 Stage 2 Introduction Generalized Kanban Assembly strategies Properties Conclusion Generalized Kanban assembly with Independent release (GKI) P1 S1 P2 MP1 P3 S3 S2 A3 A4 MP3 B1 K1 MP2 D4 D31 B3 K3 D32 B2 K2 demand

  11. May 20-25, 2005 – Zakynthos Island, Greece LA2I Introduction Generalized Kanban Assembly strategies Properties Conclusion Properties

  12. May 20-25, 2005 – Zakynthos Island, Greece LA2I K1 K2 K3 Introduction Generalized Kanban Assembly strategies Properties Conclusion Invariance properties : GKS Several closed sub-networks P1 S1 P2 MP1 P3 S2 S3 A3 A4 MP3 D3 MP2 D4 B1 B3 K1 B2 K3 K2 demand

  13. May 20-25, 2005 – Zakynthos Island, Greece LA2I S2 +K3 S1 +K3 Introduction Generalized Kanban Assembly strategies Properties Conclusion Invariance properties : GKS Several closed sub-networks P1 S1 P2 MP1 P3 S2 S3 A3 A4 MP3 D3 MP2 D4 B1 B3 K1 B2 K3 K2 demand

  14. May 20-25, 2005 – Zakynthos Island, Greece LA2I MP1 K1 B1 K1 P1 S1+K3 P2 S2+K3 MP2 K2 B2 K2 P3 S3 MP3 K3 B3 K3 A3  K3 P1 S1 P2 D3 K3+min(S1, S2) MP1 P3 S2 S3 A3 A4 MP3 D3 MP2 D4 B1 B3 K1 B2 K3 K2 demand Introduction Generalized Kanban Assembly strategies Properties Conclusion Invariance properties : GKS

  15. May 20-25, 2005 – Zakynthos Island, Greece LA2I P1 P2 MP1 P3 A3 A4 MP3 B1 MP2 D4 D31 B3 D32 B2 demand Introduction Generalized Kanban Assembly strategies Properties Conclusion Invariance properties : GKI Same bounds except that: D31 S1 + K3 D32 S2 + K3

  16. May 20-25, 2005 – Zakynthos Island, Greece LA2I Dn I1,n O1,n 1,n I3,n O3,n I4,n 3,n I2,n O2,n 2,n Relations between occurrence time of these events Evolution equations Introduction Generalized Kanban Assembly strategies Properties Conclusion Time evolution ofGKS and GKI models For GKS and GKI models : Stage 1 Stage 3 Stage 2

  17. May 20-25, 2005 – Zakynthos Island, Greece LA2I Stage 1 I1,n O1,n 1,n Stage 3 Dn I3,n O3,n I4,n Stage 2 3,n I2,n O2,n 2,n 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 = si,n+max(Ii,n, Oi,n-1) for i=1,2,3 Introduction Generalized Kanban Assembly strategies Properties Conclusion Evolution equations of GKS models

  18. May 20-25, 2005 – Zakynthos Island, Greece LA2I Stage 1 I1,n O1,n 1,n Stage 3 Dn I3,n O3,n I4,n Stage 2 3,n I2,n O2,n 2,n Introduction Generalized Kanban Assembly strategies Properties Conclusion Evolution equations of GKI models 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 = si,n+max(Ii,n, Oi,n-1) for i=1,2,3

  19. May 20-25, 2005 – Zakynthos Island, Greece LA2I Introduction Generalized Kanban Assembly strategies Properties Conclusion Comparison of GKS and GKIsystems evolution Ii,nI Ii,nS i=1,2,3 Oi,nI Oi,nS i=1,2,3 with DnI = DnS Response time of a GKI system  Response time of a GKS system

  20. May 20-25, 2005 – Zakynthos Island, Greece LA2I I’i,n Ii,ni=1,2,3,4 O’i,n Oi,ni=1,2,3  Value of one parameter  Response time Introduction Generalized Kanban Assembly strategies Properties Conclusion Influence of the parameters For GKS and GKI systems :

  21. May 20-25, 2005 – Zakynthos Island, Greece LA2I 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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