Linear Programming Application for Production Planning in Semiconductor Manufacturing

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1 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

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1

Linear Programming Application
for Production Planning in
Semiconductor Manufacturing

공장자동화연구실

이기창

1998/04/07

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Introduction(1/3)


Semiconductor manufacturing processes

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Introduction(2/3)


Characteristics of semiconductor manufacturing


Complexities


Cyclic processes


Several different recipes


Uncertain yields


Characteristics of production planning


Variable flow time


Time
-
consuming production planning

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Introduction(3/3)


Favored objective function


Demand satisfaction


Maximum utilization


Maximum throughput


Terminology


Wafer fab : front
-
end manufacturing facility


Wafer : individual unit of processing material


Die : integrated circuit

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Research overview


Golovin(1986)
-

integrated mathematical
formulation


Leachman(1992)
-

general modeling framework


Uzsoy(1992)
-

a review


Katayama(1996)
-

variable yield rate evaluation


Lee(1997)
-

variable cycle time

6

A Production Planning Methodology
for Semiconductor Manufacturing
based on Iterative Simulation and
Linear Programming Calculations

Yi
-
Feng Hung and Robert C.Leachman

Dep. Of Industrial Engineering, National Tsing Hua University,
Taiwan.

Engineering Systems Research Center, University of California at
Berceley, USA.


IEEE Transactions on semiconductor manufacturing, Vol.9,
No.2, 1996

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Assumptions of LP formulation


Demands, capacities and production rates in a planning period are constant.


Release quantity in a period is to be distributed uniformly over the period.


Production variable is quantity of a wafer type to be released in a period.


Inventory variable is inventory level of a wafer type at the end of a period.


Backorders are allowed with costs.


Workload includes machine hours due to WIP and planned releases.

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Basic LP formulation


Max


die output
revenue

-

raw
material cost

-

die
inventory
holding cost

-

cost of backordered

die demands


Subject to


m/c hours for
new releases

<=
available

m/c hours
-

m/c hours for
WIP


die output

during the period +
inventory

at the start of
period
-

backorders

at the start of period
-

inventory

at
the end of period +
backorders

at the end of period =
demands

during the period

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Notation

: # of working days on route i from start of period 1

until the end of period p

: smallest index p such that

: the expected flow time from wafer release to operation l

occurring at epoch of route i

: the expected flow time from wafer release to finish

occurring at epoch of route i

: wafer release quantity for route i in period p

: wafer quantity consuming M/C hours at operation l of route i

in period p

: wafer quantity from route i in period p

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Loads representation in terms of
release variables (1/2)

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Loads representation in terms of
release variables (2/2)

Case (1)

Case (2)

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Simulation model


Test data set


Micron Technology


10 types of products(wafers)


2 types of demands (customer order and potential sales)


Each route has 86~187operations including 30
workstations


Assumption


Each workstation have MTBF and MTTR parameters.


All operations are lot
-
based(size 50 wafers).

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Iterative scheme


Approach


To embed flow times predicted by simulation in an LP model


To convert wafer release of LP to discrete lots of simulation model


To run a simulation model using the release schedule from the LP


To collect statistics on flow time during simulation run

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Computational experiments (1/6)


Deterministic simulation model

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Computational experiments (2/6)

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Computational experiments (3/6)

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Computational experiments (4/6)


Simulation model with machine failures

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Computational experiments (5/6)

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Computational experiments (6/6)

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Conclusion


Iterative planning calculation generates accurate
production plan.


Calculation time is applicable to real shop.


2 hours for one iteration


7 iterations is enough to get acceptable flow time
agreement


Analytical model instead of simulation model
could be developed.


Alternative machine types are to be included.

21

A New Formulation Technique for
Alternative Material Planning
-

An
Approach for Semiconductor Bin
Allocation Planning

Y.F.Hung and Q.Z.Wang

Dep. Of Industrial Engineering, National Tsing Hua
University, Taiwan, ROC.


Computers and Industrial Engineering, Vol.32,
No.2, 1997.

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Alternative material planning


Formulating as transportation problem

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Alternative material planning


Formulating as transshipment problem

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Conventional bin allocation allocation
planning formulation(1/2)

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Conventional bin allocation allocation
planning formulation(2/2)

Objective function

(1) Bin inventory balance

(2) Allocation constraint

(3) Demand constraint

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New formulation for bin allocation
planning(1/2)

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New formulation for bin allocation
planning(2/2)

(2) Demand constraint

(1) Acceptable bin constraint

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Acceptable material set generation
procedure


Step1


Determine the set of supply nodes for each demand
node.


Step2


Whenever S
k1
=S
k2

and k
1

k
2
, D
k1
=D
k1


D
k2


Step3


Whenever there exists a s such that s in S
k1
, s in S
k2

S
k1
US
k2

is new supply set, S
k
=S
k1


S
k2
, D
k
=D
k1


D
k2


Step4


Whenever S
k1



S
k2
, D
k1
=D
k1

D
k2

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Example(1/3)

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Example(2/3)

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Example(3/3)

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Saving of new formulation over the
conventional one

Conventional formulation

New formulation

Number of

constraints

Number of

variables

3M

M(M+1)/2+2M

3M
-
1

2M

Straight downbinning case

Conventional formulation

New formulation

Number of

constraints

Number of

variables

M+2N

2M+N< < M+N+MN

N+M< <2^M
-
1

M+N

Non
-
straight downbinning case

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Conclusion


New formulation technique for alternative
material planning problem is presented.


Network for all periods is decomposed to separate
independent network for each period.


New technique needs 2/3 of the rows of
formulation by conventional technique.


Detailed production plan is generated each period
incorporating update WIP and demand data.