©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012

Flow Line Theory and Applications

James R. Morrison

Industrial and Systems Engineering

IEEE CASE 2012 – August 20, 2012 – Seoul, South Korea

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 2

Acknowledgements

• Much of the work discussed here was developed with – PhD candidate Kyungsu Park

– PhD candidate Woo-sung Kim

• Several of the slides were prepared by – PhD candidate Kyungsu Park

– PhD candidate Woo-sung Kim

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

t1

…

…

Customers Arrive

P2

t2

PM

tM

Customers Exit

…

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 6

Flow Lines (2)

• Buffers can be considered as a process module with zero process time

P1

t1

…

…

Customers Arrive

P2

t2

PM

tM

Customers Exit

…

P3

t3

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 7

Flow Lines (3)

• There may be multiple servers devoted to each process

P1

t1

…

…

Customers Arrive

t2 tM

Customers Exit

…

t3

R1=2 P2

R2=1

P3

R3=3 PM

RM=2

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 8

Flow Lines (4)

• Each customer may have its own class (c)

P1

tc1

…

…

Customers Arrive

tc2

tcM

Customers Exit

…

tc3

R1=2 P2

R2=1

P3

R3=3 PM

RM=2

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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] 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

[1]

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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 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

Deterministic

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 Single server Exact

(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

multi class Single server Exact Setup Exit time

Proportional multi class

K. Park et. al (2012) Multi class Multi servers Upper Bound Setup Exit time

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

t1

…

…

Customers Arrive

P2

t2

PM

tM

Customers Exit

…

P3

t3

.,max1

1

1

BM

M

m

mkMkcakc tt

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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.”

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

P1

t1

…

…

Customers Arrive

t2 tM

Customers Exit

…

t3

R1=2 P2

R2=1

P3

R3=3 PM

RM=2

)(

max

1

)(max,max)(i

Ni

M

m

mkikEakE tt

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

P1

tc1

…

…

Customers Arrive

tc2

tcM

Customers Exit

…

tc3

R1=2 P2

R2=1

P3

R3=3 PM

RM=2

M

ki

wc

i

M

ki

wc

iMk

M

ki

kwRwc

i

M

ki

wc

iMk

M

i

wc

iw

wE

kwRwE

a

wE

)1()(

,...,1

1

)),('()(

,...,1

1

)(

max)1(

,)),('(max

,

max)(

tt

tt

t

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

t1

…

…

Customers Arrive

P2

t2

PM

tM

Customers Exit

…

P3

t3

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11

t1 t4 t6 t10 t2 t3 t5 t7 t8 t9 t11

Channel 1 Channel 2 Channel 3

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11

t1 t4 t6 t10 t2 t3 t5 t7 t8 t9 t11

Channel 1 Channel 2 Channel 3

DkBB

kSk ,max1Y,minY33

max

3tt

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

tc1

…

…

Customers Arrive

P2

tc2

PM

tcM

Customers Exit

…

P3

tc3

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11

tc1 tc

4 tc6 tc

10 tc

2 tc3 tc

5 tc7 tc

8 tc9 t11

Channel 1 Channel 2 Channel 3

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

t1

…

…

Customers Arrive

P2

t2

PM

tM

Customers Exit

…

P3

t3

Ys1(k)

Ys2(k)

Ys3(k)

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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?

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

Scanner P6

Pre-scan track

Post-scan track

Buffer

Buffer

Wafers Enter

Wafers Exit

Wafer handling robots

P1

P1

P2

P2

P2

P3

P4

P4 P5

P7

P8

P8

P8

P9

P9 P10

P11

P11

P11

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/

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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)

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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

©2012 – James R. Morrison – IEEE CASE – Seoul, Korea – August 20, 2012 – 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