1. 20.03.2003Gökhan METAN1 Batching Policy in Kanban Systems U. S. Karmarkar, S. Kekre

2. 20.03.2003Gökhan METAN2 Outline n Kanban System n Markovian Models of – Single-Card Kanban System – Dual-Card Kanban System – Two-Stage Kanban System n Numerical Example n Conclusion

3. 20.03.2003Gökhan METAN3 Kanban System The Kanban system is an information system that harmoniously controls the production of the necessary products in the necessary quantities at the necessary time in every process of a factory and also among companies, which is known as the JIT production.[Monden] A Kanban is a tool to achieve JIT production. It is simply a card which is usually put in a rectangular vinyl envelope.[Monden] The pull system means that materials are drawn or sent for by the users of the material as needed.[Hall] Two types of Kanban cards in general: - Production-Ordering Kanban (or simply Production Kanban) - Withdrawal Kanban (Conveyance or Transportation Kanban)

4. Production Cards Move Cards Move Card Production Card Outbound Stockpoint Inbound Stockpoint Two Card Kanban System

5. 20.03.2003Gökhan METAN5 Important properties of Kanban System n Production is carried out in multiples of a minimum quantity or batch. n The number of cards (or containers) in the system is fixed, hence the total quantity of on-hand and on-order inventory in the facility is also fixed (fixed-volume pull system). n Production is only initiated when finished inventory is removed from the cell, thereby releasing a card (or container).

6. 20.03.2003Gökhan METAN6 Analyzed System Configurations n Single Card Kanban System: – The production activity within the cell is controlled by the Production Kanban cards, but transportation activity from the cell is not controlled by the Withdrawal (transportation) Kanban cards. – Since the production within the cell is controlled by the Kanban cards, there is an upper bound on the quantity in the cell. – Since the transportation is not controlled by the Kanban cards there is no limit for the demand from the cell, which implies there is no upper bound back orders (unfilled demand) that can accumulate.

7. 20.03.2003Gökhan METAN7 n Dual Card Kanban System: – The only difference from the above is that there is an upper bound on the back orders, which is limited by the number of transport Kanbans, since they are controlled by the withdrawal Kanban cards. n Two-stage Kanban System: – Consists of two cells in series. – Simplest version of a multistage Kanban controlled process. – Interactions can be determined in order to get insights. Analyzed System Configurations

8. 20.03.2003Gökhan METAN8 Model & Basic Assumptions n Three system configurations are both analyzed by Markovian models. – The state of the system is represented by the number of Kanban cards on order, the number of cards and batches in finished inventory, and the number of batches on back order. – Models are used to link the system parameters (batch size & number of cards) with the expected costs of operating the system. – The considered cost types are holding & back order or shortage costs. – The inventory holding cost depends on the production lead times in the cell.

9. 20.03.2003Gökhan METAN9 n The assumptions are: – Demand (D) ~ Poisson Process – Free cards enter the process queue – Production Process (P) ~ Exponential Distribution – Cell producing a single-item class – As batch sizes change  demand arrival & production rates are adjusted accordingly – The inputs to the production process (raw material or labor) are always available Model & Basic Assumptions

10. 20.03.2003Gökhan METAN10 Single-Card Kanban System

11. 20.03.2003Gökhan METAN11 Single-Card Kanban System i µ N210-2 µµµµµ λλλλλλ # of Batches of Inventory# of Batches of Backlogged Demand Markovian Model of a Single-Card Cell with N Cards Semi-infinite Birth/Death Process

12. 20.03.2003Gökhan METAN12 Single-Card Kanban System

13. 20.03.2003Gökhan METAN13 Single-Card Kanban System

14. 20.03.2003Gökhan METAN14 Single-Card Kanban System Service level factor that captures the weight given to back orders relative to inventory holding

15. 20.03.2003Gökhan METAN15 Dual-Card Kanban System -M µ N210-2 µµµµµ λλλλλλ # of Batches of Inventory# of Batches of Backlogged Demand Markovian Model of a Dual-Card Cell with N Production Cards & M Withdrawal Kanban Cards Truncated Birth/Death Process

16. 20.03.2003Gökhan METAN16 Dual-Card Kanban System

17. 20.03.2003Gökhan METAN17 Dual-Card Kanban System

18. Two-Stage Kanban System Stage-2 Container Stage-1 Container Stage-2 Output Stage-1 Output STAGE-2STAGE-1 λ μσ E2E1F2

19. 20.03.2003Gökhan METAN19 Two-Stage Kanban System

20. 20.03.2003Gökhan METAN20 Two-Stage Kanban System λλλ λλλ λλλ λλλ λλλ λλλ μ μ μ μ μ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σσσσ 012iI 0 1 2 j J # of Full Stage-1 Containers # of Full Stage-2 Containers Stage-1 Processing Blocked State Transition Diagram for Markovian Model of Two-Stage Kanban System

21. 20.03.2003Gökhan METAN21 Two-Stage Kanban System

22. 20.03.2003Gökhan METAN22 Two-Stage Kanban System

23. 20.03.2003Gökhan METAN23 Two-Stage Kanban System Analysis of Results: - For large Q, the inventory holding costs for both stage 1 & 2 grow asymptotically linearly with Q. This is because λ, μ, σ stay in the same relative position as Q increases and the transition probabilities stabilize. - When Q decreases, shortage costs rise for any choice of Kanban card numbers. This is because of the fact that the production lead times increases in the sense of Setup Times.

24. 20.03.2003Gökhan METAN24 n The batch size associated with each card has a significant effect on the performance of the Kanban system. n The effect of the number of Kanban cards in the system is also significant. n In fact, since the batch size and lead times are correlated, its effect is much more complex than the number of containers in the system. Conclusion

25. 20.03.2003Gökhan METAN25 n In multistage Kanban system, the parameters at one stage affect the performance at other stages. Increasing the number of cards at one stage leads to an increase in inventory levels at a succeeding stage, and reduces the inventory levels at a preceding stage. Conclusion

26. 20.03.2003Gökhan METAN26 References n Y. Monden. Toyota Production System, Industrial Engineering and Management Press, Norcross, Georgia, 1983. n W.R. Hall. Zero Inventories, Dow Jones, Irwin Illinois, 1983. n U.S. Karmarkar, S. Kekre. “Batching Policy in Kanban Systems”, Journal of Manufacturing Systems, Vol. 8, No. 4.