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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 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

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©2013 – James R. Morrison – UIUC ISE Seminar – 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

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 5 Flow Lines (1) Flow line with a single server for each process and one customer class – Customers require service from all processes P 1, P 2, …, P M – Service time required from process P i is i (it may be random) – Random arrivals and an infinite buffer before the first process – Finite buffers at the intermediate processes – Manufacturing blocking P1P1 11 …… Customers Arrive P2P2 22 PMPM MM Customers Exit …

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 6 Flow Lines (2) Buffers can be considered as a process module with zero process time P1P1 11 …… Customers Arrive P2P2 22 PMPM MM Customers Exit … P3P3 33

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 7 Flow Lines (3) There may be multiple servers devoted to each process P1P1 11 …… Customers Arrive 22 MM Customers Exit … 33 R 1 =2 P2P2 R 2 =1 P3P3 R 3 =3 PMPM R M =2

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 8 Flow Lines (4) Each customer may have its own class (c) P1P1 c1c1 …… Customers Arrive c2c2 cMcM Customers Exit … c3c3 R 1 =2 P2P2 R 2 =1 P3P3 R 3 =3 PMPM R M =2

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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] [2] [3] [1]

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 11 Literature on Flow Lines (2) Studied since the 1960’s Selected papers below Process Time Paper Class of customer Single/ Multi server Exact/Bounds /Approximation Setup Considered Performance metric Etc Random Lau (1986)Single classSingle serverExactNo setupThroughput2 servers Hildebrand (1956)Single classSingle serverExactNo setupThroughput3 servers Mute (1973)Single classSingle serverBoundNo setupThroughput2 or 3 servers Gershwin ( 1987)Single classSingle serverApproximationNo setupThroughputRandom failures Deterministic B. Avi-Itzhak (1965)Single classSingle serverExactNo setupExit time Infinite buffer before 1 st process Altiok and Kao (1989)Single classSingle serverExactNo setupExit time finite buffer before 1 st process J. Morrison (2010)Single classSingle server Exact (Decomposition method) SetupExit time State-dependent setup considered K. Park et. al (2010)Single ClassMulti serversUpper BoundNo setupExit time J. Morrison (2011) Proportional multi class Single serverExactSetupExit time Proportional multi class K. Park et. al (2012)Multi classMulti serversUpper BoundSetupExit time

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 12 Literature on Flow Lines (3) Avi-Itzhak (1965) – Random customer arrivals and deterministic service times Theorem: Exact recursion for customer completion (exit) times – c M (k) is the completion time of customer k from process M – a K is the arrival time of customer k to the system – B is the bottleneck process time P1P1 11 …… Customers Arrive P2P2 22 PMPM MM Customers Exit … P3P3 33

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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.”

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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 – (i) max is the bottleneck process time for those processes with i servers – Conjecture that this is an exact result P1P1 11 …… Customers Arrive 22 MM Customers Exit … 33 R 1 =2 P2P2 R 2 =1 P3P3 R 3 =3 PMPM R M =2

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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 P1P1 c1c1 …… Customers Arrive c2c2 cMcM Customers Exit … c3c3 R 1 =2 P2P2 R 2 =1 P3P3 R 3 =3 PMPM R M =2

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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 P1P1 11 …… Customers Arrive P2P2 22 PMPM MM Customers Exit … P3P3 33 P1P1 P2P2 P3P3 P4P4 P5P5 P6P6 P7P7 P8P8 P9P9 P 10 P 11 11 44 66 10 22 33 55 77 88 99 11 Channel 1Channel 2Channel 3

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 18 Exact Decompositions (2) Behavior of a customer in a channel can be characterized Theorem: Recursion for customer delay in a channel – Y 3 (k) is the delay experienced by customer k in 3 rd channel – k is the k th inter-entry time to the last channel, {.} + := max{ 0,.} Theorem: Channel delays are sufficient information P1P1 P2P2 P3P3 P4P4 P5P5 P6P6 P7P7 P8P8 P9P9 P 10 P 11 11 44 66 10 22 33 55 77 88 99 11 Channel 1Channel 2Channel 3

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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 P1P1 c1c1 …… Customers Arrive P2P2 c2c2 PMPM cMcM Customers Exit … P3P3 c3c3 P1P1 P2P2 P3P3 P4P4 P5P5 P6P6 P7P7 P8P8 P9P9 P 10 P 11 c1c1 c4c4 c6c6 c 10 c2c2 c3c3 c5c5 c7c7 c8c8 c9c9 11 Channel 1Channel 2Channel 3

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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 P1P1 11 …… Customers Arrive P2P2 22 PMPM MM Customers Exit … P3P3 33 Y 1 (k) Y 2 (k) Y 3 (k)

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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?

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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 Clustered photolithography tool [1] HIS iSuppli April 2011, [2] Elpida Memory, Inc., available at [3]

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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)

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 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

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©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 28 References

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