Report

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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 2 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 3 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 4 Flow Lines (1) … … • Flow line with a single server for each process and one customer class P1 Customers Arrive – – – – – P2 PM … t1 t2 tM Customers Exit 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 5 Flow Lines (2) … … • Buffers can be considered as a process module with zero process time P1 Customers Arrive P2 P3 PM … t1 t2 t3 tM ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 6 Customers Exit Flow Lines (3) … … • There may be multiple servers devoted to each process P1 R1=2 Customers Arrive P2 R2=1 P3 R3=3 PM RM=2 Customers Exit … t1 t2 t3 tM ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 7 Flow Lines (4) … … • Each customer may have its own class (c) P1 R1=2 Customers Arrive P2 R2=1 P3 R3=3 PM RM=2 Customers Exit … tc1 tc2 tc3 tcM ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 8 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 9 Literature on Flow Lines (1) • Flow lines serve as prototype models – – – – Automobile assembly plants Printed circuit board manufacturing Production lines Manufacturing equipment [1] • 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] 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 10 Literature on Flow Lines (2) • Studied since the 1960’s • Selected papers below Process Time Paper Class of customer Single/ Exact/Bounds Multi server /Approximation Setup Considered Performance metric Etc Lau (1986) Single class Single server Exact No setup Throughput 2 servers Hildebrand (1956) Single class Single server Exact No setup Throughput 3 servers Mute (1973) Single class Single server Bound No setup Throughput 2 or 3 servers Gershwin ( 1987) Single class Single server Approximation No setup Throughput Random failures B. Avi-Itzhak (1965) Single class Single server Exact No setup Exit time Infinite buffer before 1st process Altiok and Kao (1989) Single class Single server Exact No setup Exit time finite buffer before 1st process J. Morrison (2010) Single class Exact Single server (Decomposition method) Setup Exit time State-dependent setup considered K. Park et. al (2010) Single Class Multi servers Upper Bound No setup Exit time J. Morrison (2011) Proportional Single server multi class Exact Setup Exit time Upper Bound Setup Exit time Random Deterministic K. Park et. al (2012) Multi class Multi servers ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 11 Proportional multi class Literature on Flow Lines (3) • Avi-Itzhak (1965) … … – Random customer arrivals and deterministic service times P1 Customers Arrive P2 P3 PM … t1 t2 t3 tM Customers Exit • Theorem: Exact recursion for customer completion (exit) times c M k 1 max a k 1 t m , c M k t B . m 1 M – 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 12 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.” ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 13 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 14 Exit Time Recursions (1) • Park and Morrison (CASE 2010) … … – Allow multiple servers for each process (one customer class) P1 R1=2 P3 R3=3 P2 R2=1 Customers Arrive PM RM=2 Customers Exit … t2 t1 tM t3 • Theorem: Recursive bound for customer completion (exit) times E ( k ) max a k M t m 1 m , max E ( k i ) t i N (i ) max – t(i)max is the bottleneck process time for those processes with i servers – Conjecture that this is an exact result ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 15 Exit Time Recursions (2) • Park and Morrison (CASE 2012) … … – Allow multiple classes of customers, but prevent overtaking P1 R1=2 Customers Arrive P2 R2=1 P3 R3=3 PM RM=2 Customers Exit … tc1 tc2 tcM tc3 • Theorem: Recursive bound for customer completion (exit) times M c(w) a t w i 1 i , M M c(w) c ( w R ' ( w , k )) E ( w ) max max E ( w R ' ( w , k )) t i t i ik i k 1 k 1 ,..., M M M E ( w 1) max t ic ( w ) t ic ( w 1 ) ik ik k 1 ,..., M ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 16 , Exact Decompositions (1) • Morrison (T-ASE 2010) returns to the model of Avi-Itzhak … … – One server per process, one class of customer P1 Customers Arrive P2 P3 PM … t1 t2 t3 tM Customers Exit • System can be decomposed into segments called channels Channel 1 P1 t1 Channel 2 P2 P3 t2 t3 P4 t4 P5 t5 Channel 3 P6 t6 P7 P8 P9 t7 t8 t9 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 17 P10 t10 P11 t11 Exact Decompositions (2) • Behavior of a customer in a channel can be characterized Channel 1 P1 t1 Channel 2 P2 P3 t2 t3 P4 P5 t4 t5 Channel 3 P6 t6 P7 P8 P9 t7 t8 t9 P10 t10 • Theorem: Recursion for customer delay in a channel Y 3 k min S 3 max ,Y 3 k 1 t B max t B , D k – 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 18 P11 t11 Exact Decompositions (3) • Morrison (T-ASE 2011) allows multiple customer classes … … – Proportional service requirements P1 Customers Arrive P2 P3 PM … tc1 tc2 tc3 tcM Customers Exit • System can again be decomposed into channels and their delay Channel 1 P1 t c1 Channel 2 P2 P3 tc2 tc3 P4 tc4 P5 tc5 Channel 3 P6 t c6 P7 P8 P9 tc7 tc8 tc9 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 19 P10 tc10 P11 t11 Buffer Occupation Probabilities (1) • Kim and Morrison (TBD): Markovian model for the system … … – Use discrete time system model with geometric arrival process P1 Customers Arrive P2 P3 PM … t1 t2 t3 tM Customers Exit • Multi-dimensional Markov Chain – Each dimension describes the delay in each channel for a customer Ys3(k) Ys2(k) Ys1(k) ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 20 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? ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 21 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 22 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 Wafers Enter P1 P1 P2 P2 Buffer Scanner P6 P4 P3 P5 P4 P2 Wafer handling robots P11 Wafers Exit P11 P11 P9 P10 P8 P8 P9 P7 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/ ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 23 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 24 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) ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 25 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 26 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 ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 27 References ©2013 – James R. Morrison – UIUC ISE Seminar – August 22, 2013 – 28