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Material Handling Tools for a Discrete Manufacturing System: A Comparison of

Optimization and Simulation Frank Werner

Fakultät für Mathematik OvGU Magdeburg, Germany

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(Joint work with Yanting Ni, Chengdu University, China)

Overview of the Talk • Introduction • Literature Review • Markov Decision Process Model • Dynamic Programming Algorithm • Numerical Experiments • Conclusion

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Introduction

Background: • A material handling tool (MHT) is one of the

essential components in a manufacturing system. • MHTs are responsible for the transitions of the

lots between the stations. • The strategy of MHTs will impact the delivery

rate, cycle time and WIP level.

3

Introduction

• A Markov decision process (MDP) will be applied to model the MHT system.

• A dynamic programming algorithm will be used to solve this problem.

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Introduction Two contributions are discussed in this paper:

• A systematic management method of MHTs under a

discrete manufacturing will be developed using a Markov decision process. The quantified relationships between MHTs and WIP will be discussed within the constant WIP (CONWIP) methodology and constant demand.

• The dynamic MHT replenishment method of MHTs will be discussed within the theory of Little’s law.

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Literature Review • Many approaches for analyzing the performance

of MHTs have been proposed, etc.: • Huang et al. (2011) study the vehicle allocation

problem in a typical 300 mm wafer fabrication. They formulate it as a simulation-optimization problem and propose a conceptual framework to handle the problem.

• Chang et al. (2014) study the vehicle fleet sizing problem in semiconductor manufacturing and propose a formulation and a solution method to facilitate the determination of the optimal vehicle fleet size that minimizes the vehicle cost while satisfying time constraints.

Literature Review • To overcome the shortcomings of simulation, some

mathematical models are developed to quantify the parameters of a material handling system (MHS), such as a queuing theory model, queuing network model and a Markov chain model.

• Nazzal and McGinnis (2008) model a multi-vehicle material handling system as a closed-loop queuing network with finite buffers and general service times.

• Zhang et al. (2015) propose a modified Markov chain model to analyze and evaluate the performance of a closed-loop automated material handling system .

MDP Model System Analysis • In a discrete manufacturing factory, there exist many

types of MHTs to carry the working lots between different stages.

• There might exist only two possible scenarios for each individual workstation - an MHT change or no change.

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System Analysis

LoadUpload ProcessingProcessing

Machine

LotLot

MHT X (Y)MHT X (Y)

LotLot

MHT X (Y)MHT X (Y)

1.MHT no Change – Single Cycle

2.MHT Change – Two-Loop Cycle

LoadUpload ProcessingProcessing

Machine

MHT XMHT X

LotLot

MHT YMHT Y

Empty MHTEmpty MHTEmpty MHTEmpty MHTMHT XBUFFERMHT X

BUFFERMHT Y

BUFFERMHT Y

BUFFER

MHT XBUFFERMHT X

BUFFER

iM

iM

LotLot …....…....

LotLotLotLot …....…....

MDP Model

Figure 1: MHT Cycle Classification

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MDP Model

Some basic notations:

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MDP Model Assumptions: (1) The processing time at each station is constant, and

production meets an M/G/1 queuing system. (2) A lot arrives according to an exponential distribution

with the associated parameter . (3) Each MHT transports the lots based on the FIFO (first-

in-first-out) rule. (4) The loading time, the unloading time and the running

speed of the vehicles have a deterministic value, and both acceleration and deceleration of vehicles are ignored.

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λ

MDP Model Assumptions (cont’d): (5) The WIP quantity meets the CONWIP scenario

and the desired WIP level is . (6) The route of the MHT at a specific work station

for one specific product is fixed within the product design period.

(7) The delivery quantity is aligned with the demand of the master production schedule (MPS).

(8) Only one product is considered in this paper. 12

*w

MDP Model

TS

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MDP Model Decision times Lots of production tasks will be released based

on the numbers of available vehicles and the recycle status at each time,

where is the length of the defined production cycle.

T

{ }+= 0,1,2,...,t T L L∈ ∈Ν

L

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MDP Model Definition of the set of states

S

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MDP Model Definition of the set of actions

A

16

MDP Model Definition of the set of actions

A

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MDP Model State transition probabilities

transP

transP

18


transP

transP

19


transP

transP

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MDP Model State transition probabilities The state will change when new lots arrive, tasks are

cancelled or a machine has a breakdown. These three events can separately occur and so the state transition probability is:

transP

transP

'( ) a b ctrans i i i i iP s s P P P= × ×

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( )' , , , , ( ) ( ) ( )= × ×a b ctrans i i i i i iP s s a k l m P k P l P m

MDP Model

Reward Function v(SA) The purpose of the vehicle management is to minimize

the penalties for late deliveries of each product and to control the WIP level in the whole line within certain lower and upper limits. We can formulate the following optimization function as:

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MDP Model Maximize the Reward Function v(SA) s.t.

( , ) tDt i iR s a e

γ−

=

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MDP Model (cont’d)

( , ) tDt i iR s a e

γ−

=

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Dynamic Programming Algorithm

• The whole set of stages are grouped into 3 parts: a bottleneck group, a front group and a backend group.

• The CONWIP methodology is used for the front group and the FIFO rule is used for backend group.

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26


27


28


29


30


31


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Dynamic Programming Algorithm Station 1 Station 2 Station k-1 Station k Station k+1 Station n-1 Station n

Stage1:

CONWIP for front stations

Stage2 to Stage k-1

Stage(k+1):

Stage(k+2) to Stage(n-1)

Stage n

0 1

( )

[ ( , )]L n

t i it i

v SA

MaxE R s a= =

=

∑∑ *( )k kf s FIFO for backend stations

*1 1( )f s

* *2 2 1 1( ) ( )k kf s to f s− −

*+1 +1( )k kf s

* *2 2 1 1( ) ( )k k n nf s to f s+ + − −

*( )n nf s* * * * * * * * * * * * *1 1 1 2 2 2 1 1 1( , ( ), , ( ),..., , ( ), , ( ),..., )t

k k k k k k nSA s a s s a s s a s s a s s+ + +=

0 1( , ,..., ,..., )t LSA SA SA SA

First: Stage k

Figure 2: Sequence graph for dynamic programming

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Experiments We implemented our approach in a 300 mm

semiconductor assembly and test factory and collected the required data for performing the experiments.

ST1: SCAM ST2: EPOXY ST3: CURE ST4: BA

ST8: Finish ST7: Test ST6: CTL ST5: BI

Wafer Store

Warehouse

Vehicle Vehicle X Y

a b c c

da a a

Figure 3: Workstation flow in the case factory

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Experiments • Experiment 1: =3.64 lots/hour

1λ

1λ

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1λ

1λ

81.000082.000083.000084.000085.000086.000087.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation

Quantity of WIP comparison (Mean)ku

7.0000

7.5000

8.0000

8.5000

9.0000

9.5000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation

Quantity of WIP comparison (Stdev)ku

6.4

6.5

6.6

6.7

6.8

6.9

7

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation

Cycle time Comparison (Mean)Day

1

1.05

1.1

1.15

1.2

1.25

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation

Cycle time Comparison (Stdev)Day

0.60.650.7

0.750.8

0.850.9

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation

Vehicle mean utilization rate (Mean)

00.020.040.060.08

0.10.120.14

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation

Vehicle mean utilization rate (Stdev)

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1λ

2λ

37


1λ

2λ

70.0000

75.0000

80.0000

85.0000

90.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


0.00002.0000

4.00006.0000

8.000010.0000

12.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


6.0000

6.5000

7.0000

7.5000

8.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


0.0000

0.20000.4000

0.6000

0.80001.0000

1.2000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


0.6000

0.7000

0.8000

0.9000

1.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


0.00000.02000.04000.06000.08000.10000.1200

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


38


1λ

3λ

39


1λ

3λ

70.0000

75.0000

80.0000

85.0000

90.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


0.00002.0000

4.00006.0000

8.000010.0000

12.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


6.0000

6.5000

7.0000

7.5000

8.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


0.0000

0.20000.4000

0.6000

0.80001.0000

1.2000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


0.6000

0.7000

0.8000

0.9000

1.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


0.00000.02000.04000.06000.08000.10000.1200

1 2 3 4 5 6 7 8 9 10 11 12 13 14

MDP+DP Simulation


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Conclusion

• The results of the experiments showed some improvements of the MDP+DP approach over simulation for the majority of the runs and confirmed that the proposed approach is both feasible and effective.

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Future work • A first extension is to generalize the model

since we simplified the model by including only one product with several stations in contrast to real complex discrete manufacturing systems.

• An effective traceability method for the MHTs for

the daily operations will be developed. In this way, we want to provide a practical method for manufacturing managers and supervisors.

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