Analysis of global and local
decision rules in a
dual kanban job shop
Rafael Diaz, Ph.D. Student, Old Dominion University
Ali Ardalan, Ph.D., Old Dominion University
Fall 2005
1
• Introduction
• Background
–
–
–
–
Content
Push System versus Pull System
Kanban system - Definitions
Flow shop versus Job shop
JIT
• The model
• Measures of performance
• Results
–
–
–
–
Customer Waiting lines
Total inventory
Input stock point inventory
Output stock point inventory
• Conclusions
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Introduction
• This study simulated the operation of four-station,
dual-kanban controlled, pure job shop that
manufactures four products.
• Products went through the four stations in a different
sequence.
• Results demonstrated that considering information
regarding the length of customer queues, improves
performance measures of both customer waiting time
and total inventory.
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Introduction
• This work analyzes the effects of four kanban
policy variables
–
–
–
–
number of kanbans
length of withdrawal cycle
priority rule
information regarding the length of the customer queues
• on four performance criteria
– average customer wait-time
– total inventory
– average of full containers in the input stock points of stations.
– average of full containers in the output stock points of stations.
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Flow Shop
C1
C2
C3
C4
C1 C2
C1
C2
C1 C2
C1
C2
Raw Material
C3
Job Shop
C1 C2
C4
C2
C1
C1
C1 C2
C1
C2
C2
Raw Material
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Just In Time - JIT
• JIT refers to a scheduling system that minimizes inventory by having
material arrive just as it is about to be put in use.
• To accomplish its goal, it is necessary to design production systems
wherein required materials are made available on the production floor
exactly when is needed.
• JIT systems use containers and cards (kanbans).
• A dual-kanban system has two types of cards: production and
withdrawal card.
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Kanban System – Definitions
•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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JIT Dual-Card Kanban Job Shop
C1
C1
C1
C1
O2
C2
C2
C2
C2
C1
O1
4
C2
O3
O2
Raw
Material
C1
C1
C2
C2
C1
C1
C2
C2
3
Withdrawal Card
Assigned to take
Material inventories
C1
C1
Production Card
Assigned to produce
Part 1 or Part2
Fall 2005
Empty Containers
2
Full Containers
1
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JIT - Recent Studies
• Bett et al (2005) - importance of replenishment in JIT and
investment in capital.
• Takahashi, (2004) - JIT that considered changes in the
mean and variance of demand.
• Chen et al (2004) methodology for integrating supplier and
manufacturer capabilities.
• Richter et al (2003) developed a dynamic programming
solution for a general non-linear alternate deterministic
dynamic product recovery model - suppliers & customers
considered.
• Ardalan (1997) investigated the effects of local decision
rules in a dual-kanban Flow Shop.
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The Model
• Description:
– The model system consists of:
• Customer requirement arrivals
• Four manufacturing Cells
• Customer Departures
– The system produces 4 parts, each visiting different sequence
of station:
Part Sequence Plans
Part
Cell
1
3
2
1
4
2
4
1
2
3
3
1
4
3
2
4
2
3
4
1
• Exponential and Poisson distributions for interarrival and process
times.
• Interarrival time provided about 90% utilization level.
• The study considered systems with one, two, and three kanbans.
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Description
• Description:
– The time to move between any pair of cell is 1 minute,
regardless of the distance.
– Replication length 10,000 hours. Number of
replication:100.
– Cell producing a single-item class.
– The inputs to the production process (raw material or
labor) are always available.
– Simulation Application: Arena.
– Statistical Analysis: SAS.
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The Model - Continuation
• We considered two of the most accepted priority
rules
– First In, First Out (FIFO)
– Shortest Processing Time (SPT).
• Two levels of length of customer queues
– use the information of the length of the customer
– not use this information.
• Five levels of Withdrawal Cycle, were 28, 36, 44, 52,
and 60 periods.
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Measures of performance
• The policies were evaluated with respect to
– Average customer wait time
– The total of full containers in the system
– The sum of the average number of full containers
in the input and output stock points.
• The first criterion is a measure of customer
service, and the last two criteria are
measures of WIP in the input and output
stock point
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Results
• Using full factorial analysis of variance
• Confidence levels of 95%.
• Indicated significant interaction among
the four components.
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Results – Customer Waiting Times
Using Customer
Queue Info
Without Using
Customer Queue
Info
# Kabans
SPT
FIFO
SPT
FIFO
3
24.86
31.38
38.43
54.38
2
61.72
68.11
89.96
113.68
1
423.12
422.55
540.61
463.75
SPT – Using Info
FIFO – Using Info
SPT – Without Using Info
FIFO – Without Using Info
W. Cycle = 60
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Results - Customer waiting time
• Statistically significant differences between the average wait
times.
• Overall, for those treatments that used information, results were
up to 37 % shorter than those treatments that ignored this
information.
• Effects of withdrawal cycle for treatments with one kanban were
observed more markedly.
• With one kanban - using FIFO and information performed better
than the ones that used SPT and ignored the information on the
customer waiting line.
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Customer waiting time
• A large number of kanbans increases the availability of
WIP that stations use to produce end products.
• It reduces the possibility of starvation and improves
the availability of end products.
• Short withdrawal cycle improves the station’s
responsiveness to demand The result is short
customer wait times.
• Using the information increases the likelihood of
producing the items that have real customer demand
rather than producing items just to replenish inventory.
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Total inventory
• There were interactions: number of kanbans, the withdrawal cycle,
and the priority rule.
• Treatments with 1, 2, and 3 kanbans and withdrawal cycles were
significantly different.
• There exist interactions between the number of kanbans, priority
rule, and the status of the customer line length information.
• With one kanban had significantly lower inventory levels than those
with two and three kanbans.
• Similar results for 2 and 3 kanbans.
• There is no evidence of mean differences for a treatment with one
kanban that used FIFO and those that used SPT.
• The priority rule had a minor effect on total inventory
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Input stock point inventory
• Treatments with two kanbans using FIFO or SPT
priority rule were not significantly different from each
other.
• Using the information regarding status of customer
waiting line was significantly different.
• Magnitude of the effects are number of kanbans, the
status of customer waiting line, and priority rule.
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Output stock point inventory
• Those that used the information regarding the length
of the customer queue had significantly smaller WIP
than those that ignored such information.
• Treatments with two kanbans that used the
information, those with FIFO had significantly smaller
WIP in output stock points than those with SPT.
• The analysis of all pairwise comparisons of
treatments means shows that:
– One kanban and withdrawal cycle 60: lowest level
of inventory
– Three kanbans and withdrawal cycle of 28 :
highest level of inventory.
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Output stock point inventory
• Using the information results in assigning higher priority to
production of products that have an immediate customer demand.
• Using information reduces the inventory levels in the output stock
point of station: As soon as these items are made, they will be
moved to succeeding stations..
• The priority rule FIFO results in low levels of inventory : since it
may assign a higher priority to jobs that take a long time to be
processed, therefore, it may replenish output stock point
inventory at slower rate than Short Processing Time (SPT).
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Conclusions
• Using the information regarding customer
queue length in job shops:
– It increases service levels, and
– It reduces total inventory simultaneously.
• Treatments that used the information of
customer queue length result in shorter
customer wait time.
• It is more marked when smaller number of
kanbans is used.
• Whenever the information is used, finished and semi-finished
products that have higher customer demand will be produced.
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Conclusions
• Priority rules and status of customer waiting line had a
minor effect on total inventory, treatments with FIFO that
used the information regarding the length of the
customer queue, resulted in the lowest total inventory.
• The experiments demonstrated that the input and output
stock point inventory responded similarly to the number
of kanbans and withdrawal cycle changes.
• Increasing the number of kanbans from 1 to 2, and from
2 to 3, resulted in a similar increase in both input and
outputs stock point inventories.
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Conclusions
• When the number of kanbans was reduced from two to
one for treatments with cycle of 60, the inventory
dropped significantly.
• Although customer wait time increased, when the
number of kanban was reduced from three to two, the
decrease in total inventory was disproportionately larger.
• It may be possible to decrease the number of kanbans
and have a significant decrease in WIP inventory without
severely increasing the average customer wait time.
Fall 2005
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References
•
Ardalan, Alireza, “Analysis of local decision rules in a dual-kanban Flow Shop,”
Decision Sciences, Vol. 28, No. 1 (1997), pp. 195- 211.
•
Betts, John M., and Robert B. Johnston, “Just-in-time component replenishment
decisions for assemble-to-order manufacturing under capital constraint and stochastic
demand,” International Journal of Production Economics, Amsterdam: January 28,
Vol. 95, (2005), pp. 51-70.
•
Chen, Chee-Cheng, Tsu-Ming Yeh, and Ching-Chow, Yang, “Customer-focused rating
system of supplier quality performance,” Journal of Manufacturing Technology
Management, Bradford, Vol. 15, Issue 7 (2004), pp. 599-617.
•
Richter Knut, and Barbara Gobsch, “The market-oriented dynamic product recovery
model in the just-in-time framework International,” Journal of Production Economics,
Amsterdam: January 11, Vol. 81/82 (2003), pp. 369-374.
Fall 2005
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References
•
Stephe, Shmanske, “JIT and the complementarity of buffers and lot size,” American
Business Review, West Haven: January, Vol. 21, Issue 1, (2003), pp. 100-106.
•
Takahashi, Katsuhiko, Katsumi Morikawa, and Nobuto Nakamura, “Reactive JIT
ordering system for changes in the mean and variance of demand,” International
Journal of Production Economics, Amsterdam, Vol. 92, Issue. 2 (2004), pp. 181196.
•
White, Richard E, and John N. Pearson, “JIT system integration and customer
service,” International Journal of Physical Distribution & Logistics Management,
Bradford, Vol. 31, Issue 5, (2001), pp. 313-333.
•
Yang, Jiaqin, and Richard H. Deane, “A lotsize reduction model for just-in-time
manufacturing systems,” Integrated Manufacturing Systems,Vol. 13,
Issue 7,
(2002), pp. 471-488.
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Thank you!
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