Flow Line Theory and Applications - Department of Industrial and

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 ik i  k 1 k  1 ,..., M  M M  E ( w  1)  max  t ic ( w )   t ic ( w 1 ) ik ik 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