Batching Policy in Kanban Systems U. S. Karmarkar, S. Kekre

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Batching Policy in Kanban SystemsU. S.
Karmarkar, S. Kekre
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Outline

• Kanban System
• Markovian Models of
• Single-Card Kanban System
• Dual-Card Kanban System
• Two-Stage Kanban System
• Numerical Example
• Conclusion

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Kanban System
The pull system means that materials are drawn or
sent for by the users of the material as
needed. Hall
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
Two types of Kanban cards in general -
Production-Ordering Kanban (or simply Production
Kanban) - Withdrawal Kanban (Conveyance or
Transportation Kanban)
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Two Card Kanban
System
Outbound Stockpoint
Inbound Stockpoint
Move Card
Production Card
Move Cards
Production Cards
Production Cards
Move Cards
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Important properties of Kanban System

• Production is carried out in multiples of a
  minimum quantity or batch.
• 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).
• Production is only initiated when finished
  inventory is removed from the cell, thereby
  releasing a card (or container).

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Analyzed System
Configurations

• 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.

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Analyzed System
Configurations

• 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.
• 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.

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Model Basic
Assumptions

• 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.

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Model Basic
Assumptions

• 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

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Single-Card Kanban
System
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Single-Card Kanban
System
Semi-infinite Birth/Death Process
Markovian Model of a Single-Card Cell with N Cards
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Single-Card Kanban
System
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Single-Card Kanban
System
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Single-Card Kanban
System
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Dual-Card Kanban
System
Truncated Birth/Death Process
Markovian Model of a Dual-Card Cell with N
Production Cards M Withdrawal Kanban Cards
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Dual-Card Kanban
System
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Dual-Card Kanban
System
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Two-Stage Kanban
System
STAGE-2
STAGE-1
µ
s
?
E2
E1
F2
F2
Stage-2 Container
Stage-2 Output
Stage-1 Container
Stage-1 Output
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Two-Stage Kanban
System
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Two-Stage Kanban
System
State Transition Diagram for Markovian Model of
Two-Stage Kanban System
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Two-Stage Kanban
System
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Two-Stage Kanban
System
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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 ?, µ, s 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.
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Conclusion

• The batch size associated with each card has a
  significant effect on the performance of the
  Kanban system.
• The effect of the number of Kanban cards in the
  system is also significant.
• 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.

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Conclusion

• 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.

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References

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