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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
1
(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
2
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.
4
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.
5
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
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MDP Model Definition of the set of actions
A
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MDP Model State transition probabilities
transP
transP
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MDP Model State transition probabilities
transP
transP
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MDP Model State transition probabilities
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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Dynamic Programming Algorithm
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Dynamic Programming Algorithm
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Dynamic Programming Algorithm
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Dynamic Programming Algorithm
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Dynamic Programming Algorithm
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Dynamic Programming Algorithm
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Dynamic Programming Algorithm
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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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Experiments • Experiment 1: =3.64 lots/hour
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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Experiments • Experiment 2: =4.42 lots/hour
1λ
2λ
37
Experiments • Experiment 2: =4.42 lots/hour
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
Quantity of WIP comparison (Mean)ku
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
Quantity of WIP comparison (Stdev)ku
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
Cycle time Comparison (Mean)Day
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
Cycle time Comparison (Stdev)Day
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
Vehicle mean utilization rate (Mean)
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
Vehicle mean utilization rate (Stdev)
38
Experiments • Experiment 3: =3.09 lots/hour
1λ
3λ
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Experiments • Experiment 3: =3.09 lots/hour
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
Quantity of WIP comparison (Mean)ku
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
Quantity of WIP comparison (Stdev)ku
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
Cycle time Comparison (Mean)Day
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
Cycle time Comparison (Stdev)Day
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
Vehicle mean utilization rate (Mean)
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
Vehicle mean utilization rate (Stdev)
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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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