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Demand-Driven, Iterative Capacity Allocation and Cycle Time Estimation for Re-entrant Lines

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Shi-Chung Chang

Dept. of Electrical Engineering National Taiwan University

December 8, 1999

S.-C. Chang, “ Demand-Driven, Iterative Capacity Allocation and Cycle Time Estimation for Re-entrant Lines,” Proceedings of 38th IEEE Conference on Decision and Control, Phoenix, AZ, Dec., 7-10, 1999, pp.2270~2275,

NSC-85-2622-E-002-018R, NSC-86-2622-E-002-025R.

Demand-Driven, Iterative Capacity

Allocation and Cycle Time

(2)

Outline

• Daily Target Setting Problem • Capacity Allocation

• Cycle Time Estimation • Fixed Point Iteration • Implementation Results • Conclusions

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Photo Imp Dif Dry Imp Imp Dry Dry Dif Dif Wet Wet Wet Dry CVD Wafer Start Wafer Out

Re-entrant Production

Process

Wafers revisit machines at different stages of production => Re-entrant nature

=> Resource competition among - product types

(4)

S T A G E 1 S T A G E 2 S T A G E 3 S T A G E 4 S T A G E 5 S T A G E 6 W a f e r R e l e a s e D e m a n d e d O u t p u t

Capacity Allocation Problem

=> How to allocate machine capacity to

satisfy demand, maximize wafer moves and balance the line

Given demanded output, WIP distribution and release quantity of each day

(5)

Product Types

How about

Stages

(6)

Solution Method

• Proportional Capacity Allocation by P

ull and Push Principles

• Cycle Time/Wafer Flow Estimation by

Deterministic Queueing Analysis

(7)

Pull (Backward) Procedure

j j+1

Pull Targetj = Day_demand_Movej+1 - wipj+1

+ Reference WIPj+1

• Demanded Moves Determined byMaster Product

ion Schedule

• Effects:

– to reflect MPS delay catch up force

– to provide needed WIP to downstream – to generate effective moves

(8)

Proportional Capacity Allocation

If Equipment A has total capacity 6, and

Demanded capacity Equipment type Stage i 3 A Stage j 6 A total 9 Allocated capacity Stage i 2 Stage j 4 total 6 Proportional Capacity

Allocation has the effect of

Line Balance

Proportional Capacity

Allocation has the effect of

(9)

Push (Forward) Procedure

Push targetj = Pull targetj-1 + WIPj - Pull ta

rgetj

j

Pull targetj-1 Pull targetj

• When WIP is enough, proportionally allocate

residual capacity to

– maximize machine utilization

– increase turn rate and total moves – reduce cycle time

(10)

Cycle Time/Wafer Flow Estimation

How many WIPs do

I need to achieve PULL and PUSH targets?

Available_WIPj = Initial_WIPj+ Flow_in_WIPj ==> Q: How many stages may a batch of WIP

penetrate within a day?

(11)

Stage of Penetration Estimation Algorithm

(SOPEA)

WIPj j WIPj+1j+1 WIPk-1 k-1 WIPkk



nj nj+1 nk-1 nk

R0

Tj(k-1)

T

Fact: given capacity allocation

==> decomposition by stage by part type Consider (1) single part type

(2) FIFO

(12)

SOPEA Recursion

Case 1:

T

j(k-1)

T

(j1)k

(WIP

j

-

1)

τ

k

/n

k ==>

T

jk

T

(j

-

1)k

τ

k

/n

k

Case 2:

T

j(k-1)

T

(j1)k

(WIP

j

-

1)

τ

k

/n

k ==>

T

jk

T

j(k

-

1)

WIP

j

τ

k

/n

k

(13)

Fixed Point Iteration

Initialization PULL+P.C.A. PUSH+P.C.A. FLOW_IN by SOPEA MAX_FLOW_IN

(14)

Field Implementation Results: Phase 1

• More than 10% reduction in WIP and increase in

moves

Figure 6.1(a) WIP Profile before and after Phase 1 Implementation 22 23 24 25 26 27 28 1 6 11 16 21 26 31 36 41 46 51 56 Day T ot al W IP ( x 10 00 w af er s) before after F ig u r e 6 .1 ( b ) P r o file o f D a ily T o t a l M o ve s b e fo r e a n d a ft e r P h a s e 1 Im p le m e n t a t io n 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 1 6 1 1 1 6 2 1 2 6 3 1 3 6 4 1 4 6 5 1 5 6 D a y T ot al M ov es ( x 10 00 ) After Before

(15)

Field Implementation Results: Phase 2

• Another 5% increase in moves and 10% increase in

target hit rate

Figure 6.2(b) Daily Moves and Averages before and after Phase 2 (SOPEA) Implementation

46 48 50 52 54 56 58 60 1 6 11 16 21 26 31 Day T ot al M ov es ( x 10 00 ) 78 83 88 93 98 103 1 6 11 16 21 26 31 H it R at e (% ) SOPEA SOPEA

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Conclusions

• Developed a method for daily capacity allocation

and cycle time estimation

– PULL + PUSH procedure

– Proportional resource allocation

– Recursive C. T. estimation algorithm – Fixed point iteration

• Achieved successful field implementations • Performed preliminary algorithmic analysis

數據

Figure 6.1(a) WIP Profile before and after Phase 1 Implementation2223242526272816111621263136 41 46 51 56Day
Figure 6.2(b) Daily  Moves and Averages  before and after Phase 2 (SOPEA) Implementation

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