Fall 2005 1

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 2

Content• Introduction• Background

– 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

Fall 2005 3

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.

Fall 2005 4

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.

Fall 2005 5

C1 C2 C3 C4

C2

C3

C1

C4

C2C1

C2C1

C2C1

C2C1

C2C1

C2C1

C2C1

C2C1

Raw Material

Raw Material

Job Shop

Flow Shop

Fall 2005 6

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.

Fall 2005 7

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)

Fall 2005 8

C2C1

C2C1

JIT Dual-Card Kanban Job Shop

O1

O2

O2

O3

C1

Empty Containers Full Containers

Withdrawal Card Assigned to take

Material inventories

Production Card Assigned to produce

Part 1 or Part2

C2C1

C1

Raw Material

12

3

4

C2C1

C2C1

C2C1

C2C1

C2C1

C2C1

Fall 2005 9

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.

Fall 2005 10

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:

• 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.

Part

1 3 2 1 42 4 1 2 33 1 4 3 24 2 3 4 1

Part Sequence PlansCell

Fall 2005 11

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.

Fall 2005 12

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.

Fall 2005 13

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

Fall 2005 14

Results

• Using full factorial analysis of variance

• Confidence levels of 95%.

• Indicated significant interaction among the four components.

Fall 2005 15

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

Customer Waiting Time

0

100

200

300

400

500

600

1 2 3

# Kabans

W. Cycle = 60

SPT – Using Info

FIFO – Using Info

SPT – Without Using Info

FIFO – Without Using Info

Fall 2005 16

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.

Fall 2005 17

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.

Fall 2005 18

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

Fall 2005 19

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.

Fall 2005 20

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.

Fall 2005 21

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).

Fall 2005 22

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.

Fall 2005 23

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.

Fall 2005 24

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 25

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 26

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. 181-196.

 • 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.

Fall 2005 27

Thank you!