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
Outline
• Daily Target Setting Problem • Capacity Allocation
• Cycle Time Estimation • Fixed Point Iteration • Implementation Results • Conclusions
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
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
Product Types
How about
Stages
Solution Method
• Proportional Capacity Allocation by P
ull and Push Principles
• Cycle Time/Wafer Flow Estimation by
Deterministic Queueing Analysis
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
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
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
Cycle Time/Wafer Flow Estimation
How many WIPs doI 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?
Stage of Penetration Estimation Algorithm
(SOPEA)
WIPj j WIPj+1 j+1 WIPk-1 k-1 WIPk k
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
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
Fixed Point Iteration
Initialization PULL+P.C.A. PUSH+P.C.A. FLOW_IN by SOPEA MAX_FLOW_INField 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
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
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