Recent Directions in the Theory of Flow Lines with Applications to Semiconductor Manufacturing

1. Recent Directions in the Theory of Flow Lines with Applications to Semiconductor Manufacturing James R. Morrison KAIST, South Korea Department of Industrial and Systems Engineering UIUC ISE Graduate Seminar: Thursday 3-4 pm, August 22, 2013

2. Acknowledgements • Much of the work discussed here was developed with • PhD student Kyungsu Park • PhD student Woo-sung Kim • Several of the slides were prepared by • PhD student Kyungsu Park • PhD student Woo-sung Kim

3. Flow Line Discussion Overview • System description: Flow lines • Literature review: Brief historical perspective on flow lines • Recent results on regular flow lines with random arrivals • Exit time recursions • Exact decomposition • Buffer occupation probabilities • Application opportunities in semiconductor manufacturing • Concluding remarks

4. Presentation Overview • System description: Flow lines • Literature review: Brief historical perspective on flow lines • Recent results on regular flow lines with random arrivals • Exit time recursions • Exact decomposition • Buffer occupation probabilities • Application opportunities in semiconductor manufacturing • Concluding remarks

5. Flow Lines (1) • Flow line with a single server for each process and one customer class • Customers require service from all processes P1, P2, …, PM • Service time required from process Pi is ti (it may be random) • Random arrivals and an infinite buffer before the first process • Finite buffers at the intermediate processes • Manufacturing blocking … … P1 P2 PM Customers Arrive Customers Exit … t1 t2 tM

6. Flow Lines (2) • Buffers can be considered as a process module with zero process time … … P1 P2 P3 PM Customers Arrive Customers Exit … t1 t2 t3 tM

7. Flow Lines (3) • There may be multiple servers devoted to each process P3 P1 PM R3=3 … … P2 R1=2 RM=2 R2=1 Customers Arrive Customers Exit … t2 t1 tM t3

8. Flow Lines (4) • Each customer may have its own class (c) P3 P1 PM R3=3 … … P2 R1=2 RM=2 R2=1 Customers Arrive Customers Exit … tc2 tc1 tcM tc3

9. Presentation Overview • System description: Flow lines • Literature review: Brief historical perspective on flow lines • Recent results on regular flow lines with random arrivals • Exit time recursions • Exact decomposition • Buffer occupation probabilities • Application opportunities in semiconductor manufacturing • Concluding remarks

10. Literature on Flow Lines (1) • Flow lines serve as prototype models • Automobile assembly plants • Printed circuit board manufacturing • Production lines • Manufacturing equipment • Well known application • HP printer manufacturing line redesigned using approximate decomposition models for flow lines (M. Berman, et al 1998) • Claim $280 million increase in revenue and printer shipments • New applications arising in semiconductor manufacturing [1] [1] http://www.c3systems.co.uk/wp-content/gallery/other-industries/factory-modern-robotic-assembly-line01.jpg [2] http://www.ventures-africa.com/wp-content/uploads/2012/08/Bottling-plant.jpg [3] http://cdn5.zyxware.com/files/u1948/images/2011/04/HP%20LASER%20JET(P1007)%20.jpg

11. Literature on Flow Lines (2) • Studied since the 1960’s • Selected papers below

12. Literature on Flow Lines (3) • Avi-Itzhak (1965) • Random customer arrivals and deterministic service times • Theorem: Exact recursion for customer completion (exit) times • cM(k) is the completion time of customer k from process M • aK is the arrival time of customer k to the system • tB is the bottleneck process time … … P1 P2 P3 PM Customers Arrive Customers Exit … t1 t2 t3 tM

13. Literature on Flow Lines (4) • Altiok and Kao (1989) also studied the exit behavior • Single server, single class of customer, deterministic service times • Finite buffer before the first process • Considerable past and ongoing work to extend the frontiers • Exact solutions for certain cases (e.g., 2 or 3 processes, Li et al) • Approximate decomposition methods (e.g., Gershwin et al, Li et al) • Many unanswered questions about the exact behavior • No Avi-Itzhak style recursions outside of single server, single class • From the classic text by Altiok: “[T]here are no known techniques to obtain measures specific to particular buffers, such as the probability distribution of the buffer contents.”

14. Presentation Overview • System description: Flow lines • Literature review: Brief historical perspective on flow lines • Recent results on regular flow lines with random arrivals • Exit time recursions • Exact decomposition • Buffer occupation probabilities • Application opportunities in semiconductor manufacturing • Concluding remarks

15. Exit Time Recursions (1) • Park and Morrison (CASE 2010) • Allow multiple servers for each process (one customer class) • Theorem: Recursive bound for customer completion (exit) times • t(i)max is the bottleneck process time for those processes with i servers • Conjecture that this is an exact result P3 P1 PM R3=3 … … P2 R1=2 RM=2 R2=1 Customers Arrive Customers Exit … t2 t1 tM t3

16. Exit Time Recursions (2) • Park and Morrison (CASE 2012) • Allow multiple classes of customers, but prevent overtaking • Theorem: Recursive bound for customer completion (exit) times P3 P1 PM R3=3 … … P2 R1=2 RM=2 R2=1 Customers Arrive Customers Exit … tc2 tc1 tcM tc3

17. Exact Decompositions (1) • Morrison (T-ASE 2010) returns to the model of Avi-Itzhak • One server per process, one class of customer • System can be decomposed into segments called channels … … P1 P2 P3 PM Customers Arrive Customers Exit … t1 t2 t3 tM Channel 1 Channel 2 Channel 3 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 t10 t1 t4 t6 t2 t3 t5 t7 t8 t9 t11

18. Exact Decompositions (2) • Behavior of a customer in a channel can be characterized • Theorem: Recursion for customer delay in a channel • Y3(k) is the delay experienced by customer k in 3rd channel • Dk is the kth inter-entry time to the last channel, {.}+ := max{ 0, .} • Theorem: Channel delays are sufficient information Channel 1 Channel 2 Channel 3 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 t10 t1 t4 t6 t2 t3 t5 t7 t8 t9 t11

19. Exact Decompositions (3) • Morrison (T-ASE 2011) allows multiple customer classes • Proportional service requirements • System can again be decomposed into channels and their delay … … P1 P2 P3 PM Customers Arrive Customers Exit … tc1 tc2 tc3 tcM Channel 1 Channel 2 Channel 3 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 tc10 tc1 tc4 tc6 tc2 tc3 tc5 tc7 tc8 tc9 t11

20. Buffer Occupation Probabilities (1) • Kim and Morrison (TBD): Markovian model for the system • Use discrete time system model with geometric arrival process • Multi-dimensional Markov Chain • Each dimension describes the delay in each channel for a customer … … P1 P2 P3 PM Customers Arrive Customers Exit … t1 t2 t3 tM Ys3(k) Ys2(k) Ys1(k)

21. Buffer Occupation Probabilities (2) • Conjecture: Enables exact computation of equilibrium probabilities… work in progress • Kim and Morrison (CASE 2012) include setups • State-dependent setups as in clustered photolithography tools • JIT throughput calculations: Exact analytic in some cases • JIT throughput calculations: Exact algorithmic in others (via MC) • Can the decomposition be used similarly for multiple customer classes?

22. Presentation Overview • System description: Flow lines • Literature review: Brief historical perspective on flow lines • Recent results on regular flow lines with random arrivals • Exit time recursions • Exact decomposition • Buffer occupation probabilities • Application opportunities in semiconductor manufacturing • Concluding remarks

23. Applications: Semiconductor Manufacturing Models (1) • Semiconductor manufacturing • Global revenue in 2010: US$ 304,000,000,000 • Construction cost for 300 mm fab: US$ 5,000,000,000 • Clustered photolithography tool cost: US$ 20,000,000-50,000,000 Pre-scan track Buffer P2 Scanner P6 P1 P4 Wafers Enter P3 P5 P2 P1 P4 P2 Wafer handling robots P11 P8 P9 Wafers Exit P10 P7 P11 P8 P9 P11 P8 Post-scan track Buffer Clustered photolithography tool [1] HIS iSuppli April 2011, [2] Elpida Memory, Inc., available at http://www.eplida.com, [3] http://www.rocelec.com/manufacturing/wafer_fabrication/

24. Applications: Semiconductor Manufacturing Models (2) • Equipment and fabricator simulations are used to • Predict value of changes to fabricator capacity • Predict value of changes to fabricator production control policies • Predict capacity of fabricators • Predict cost of future fabricators • … • Want expressive, accurate and computationally tractable models

25. Applications: Semiconductor Manufacturing Models (3) • Current models can be excellent: Certain tools and scenarios • Reduced wafers per lot in next generation 450mm wafer fabs • Flow line models for clustered photolithography may be more appropriate (explicitly model the issues causing these errors)

26. Presentation Overview • System description: Flow lines • Literature review: Brief historical perspective on flow lines • Recent results on regular flow lines with random arrivals • Exit time recursions • Exact decomposition • Buffer occupation probabilities • Application opportunities in semiconductor manufacturing • Concluding remarks

27. Concluding Remarks • Flow lines serve as a prototype manufacturing model • Studied and applied successfully for many years • Opportunities: Fundamental theory and new application areas • Deterministic service times and random arrivals • Exit recursions and exact decompositions • Buffer occupation probabilities and JIT throughput • Application opportunities in semiconductor manufacturing • Equipment models for clustered photolithography • Improved fidelity with acceptable computation • Future directions • Continue onward • Industry buy-in for the models and integration with decision models

28. References