1. 1 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 Estimation for Re-entrant Lines

2. 2 Outline Daily Target Setting Problem Capacity Allocation Cycle Time Estimation Fixed Point Iteration Implementation Results Conclusions

3. 3 Photo Imp Dif Dry Imp Dry Dif 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 - stages of a product type

4. 4 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. 5 Product Types How about Stages Machine types

6. 6 Solution Method Proportional Capacity Allocation by Pull and Push Principles Cycle Time/Wafer Flow Estimation by Deterministic Queueing Analysis Fixed Point Iteration

7. 7 Pull (Backward) Procedure jj+1 Pull Target j = Day_demand_Move j+1 - wip j+1 + Reference WIP j+1 Demanded Moves Determined byMaster Production Schedule Effects: –to reflect MPS delay catch up force –to provide needed WIP to downstream –to generate effective moves

8. 8 Proportional Capacity Allocation If Equipment A has total capacity 6, and Proportional Capacity Allocation has the effect of Line Balance ！

9. 9 Push (Forward) Procedure Push target j = Pull target j-1 + WIP j - Pull target j j Pull target j-1 Pull target j When WIP is enough, proportionally allocate residual capacity to –maximize machine utilization –increase turn rate and total moves –reduce cycle time ==> Target j = Pull Target j + Push target j

10. 10 Cycle Time/Wafer Flow Estimation How many WIPs do I need to achieve PULL and PUSH targets? Available_WIP j = Initial_WIP j + Flow_in_WIP j ==> Q: How many stages may a batch of WIP penetrate within a day? ==> Equivalent to finding cycle times of each stage

11. 11 Stage of Penetration Estimation Algorithm (SOPEA) Fact: given capacity allocation ==> decomposition by stage by part type Consider (1) single part type (2) FIFO (3) fractional number of machine allowed

12. 12 SOPEA Recursion Case 1: ==> Case 2: ==>

13. 13 Fixed Point Iteration Initialization PULL+P.C.A. PUSH+P.C.A. FLOW_IN by SOPEA MAX_FLOW_IN CONVERGE ? No Yes Targets (Capac. Alloc.) C. T. Estimates

14. 14 Field Implementation Results: Phase 1 More than 10% reduction in WIP and increase in moves before after

15. 15 Field Implementation Results: Phase 2 Another 5% increase in moves and 10% increase in target hit rate SOPEA

16. 16 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