Shi-Chung Chang Dept. of Electrical Engineering National Taiwan University December 8, 1999

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

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

3. Wet Dry Dif Wet Imp Imp Photo Dry Imp Dry CVD Dif Dif Wafer Out Dry Wet Wafer Start 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. Capacity Allocation Problem Given demanded output, WIP distribution and release quantity of each day => How to allocate machine capacity to satisfy demand, maximize wafer moves and balance the line

5. How about 50 Product Types 120 Stages ? 30 Machine types

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

7. j j+1 Pull (Backward) Procedure • Demanded Moves Determined byMaster Production Schedule • Effects: • to reflect MPS delay catch up force • to provide needed WIP to downstream • to generate effective moves Pull Targetj = Day_demand_Movej+1 - wipj+1 + Reference WIPj+1

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

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

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? ==> Equivalent to finding cycle times of each stage

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

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

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

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

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