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Franck FONTANILI - CGI IMSM'07
Content of the presentation
•Introduction and context•Problem•Proposed solution•Results•Conclusions and perspectives
• discrete-event simulation, genetic algorithm, multicriterion optimization
Discrete events simulation and genetic algorithm-based manufacturing
execution
Keywords
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Franck FONTANILI - CGI IMSM'07
Overview
• Manufacturing context: assembly of mixed models
• Stage of preparation of the release of a campaign
• How to determine a « good » value of control parameters ?
Introduction and context
Coupling DES and optimization algorithm
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Franck FONTANILI - CGI IMSM'07
Manufacturing system
• Free automated transfer with belt conveyors
• Manual or automated assembly operations• Workstations layout in: series or parallel
Introduction and context
Workstation #1
Loading workstation
Unloading workstation
Upstream accumulationDownstream accumulation
Loop section
Workstation #2
Workstation #3
Workstation #4
Workstation #5
Workstation #6
Belt conveyo
rs
Pallet
Coding system
Product to
assemble
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Franck FONTANILI - CGI IMSM'07
Flow of pallets
Introduction and context
5
123
4 6 5
13
4 6
22
• Non-permutable phases
• Non-redundant phases
= generalized flow-shop
• In case of saturation of one of the bypass workstations:
= loop on the central conveyor
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Franck FONTANILI - CGI IMSM'07
Assembly campaigns planning
Problem
Assembly order
Finished product
referenceQuantity Load. WS 1 WS 2 WS 3 WS 4 WS 5 WS 6 Unload.
1 A 10 3 4 2 3 5
2 C 5 3 1 4 3 2 5
3 E 8 4 3 4 5 5
4 B 15 3 4 5
5 F 6 3 1 2 3 5
A A A A A A A A A A
C C C C C
E E E E E E E E
BB B B B B B B B B B B B B B
F F F F F F
Time
Se
qu
en
ce
10 products A
5 products C
8 products E
15 products B
6 products F
Example of a
campaign
with 5 orders
Release sequencing Mixed process
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Franck FONTANILI - CGI IMSM'07
Assembly campaigns planning
Problem
Line is empty Line is empty
Implementation of values of
control parametersfor campaign n
RampUp RampDownSteady state
Preparation and optimizationof control parameters
for campaign n+1
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Franck FONTANILI - CGI IMSM'07
Flow control parameters
• Release sequence of k assemby orders
• Inter-release Time (IrTi)
Problem
AAAAAAAAAAAA BBBBB CCCCCCCC
AAAAAAAAAAAABBBBBCCCCCCCC
sequencing
1
2
3
k! combinations
120 combinations for 5 orders
(without splitting)
[maxIrTi-minIrTi+1)k
combinations
371.293 combinations for 5
orders 2 sec.<IrTi<16
sec.
BBBBB CCCCCCCC AAAAAAAAAAAA
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Franck FONTANILI - CGI IMSM'07
Flow control parameters
• Capacity of upstream conveyor on j workstations
• Number of pallets to be used (Np)
Problem
StA
m
[maxStAm-minStAm+1)j
combinations
46.656 combinations for 6
workstations 0<StAm<7
0<Np<26
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Franck FONTANILI - CGI IMSM'07
Flow control parameters
• Capacity of downstream conveyor• Priority rule on the exit of workstation• Splitting of the sequence of the assembly
orders• Etc.
Problem
With only the 3 most sensitive parameters :•Inter-Release Time (IrTi)•Capacity of upstream conveyor (StAm)•Number of pallets (Np)
More than 1011 combinations
What combination to be used ?
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Franck FONTANILI - CGI IMSM'07
Use of Simulation
• Simulation is a frequently used tool during stage of:
Design Improvement
of manufacturing systems (existent or to be built)
• Proposal: use of simulation during stage of: preparation the execution of a campaign to provide a decision-making aid for
the choice of the values to fix at the flow control parameters
Proposed solution
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Franck FONTANILI - CGI IMSM'07
Use of Simulation
• Simulation of a k order campaign on j workstations
Proposed solution
Campaign to release
Assembly order
Finished product
referenceQuantity Load. WS 1 WS 2 WS 3 WS 4 WS 5 WS 6 Unload.
1 A 10 3 4 2 3 5
2 C 5 3 1 4 3 2 5
3 E 8 4 3 4 5 5
4 B 15 3 4 5
5 F 6 3 1 2 3 5
0 sec.<IrTi(k)<13 sec.
0<StAm(j)<7
19<Np<36
Objective function
Control parameters
Simulation model
designed with Witness
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Franck FONTANILI - CGI IMSM'07
Choice of the objective function
• Optimization criteria• Total Lead Time of the campaign (Lt) between the
release of the first pallet and the delivery of the last.
• Average Work in Process (WIP) between the loading workstation and the unloading workstation
• Total number of Setup (Set) corresponding to the change over from one product to another
• Multicriterion weighted objective function
Proposed solution
Lead t. WIP SetupLead time 1 2 3
Wip 0,5 1 1Setup 0,3333 1 1Summ 1,8333 4 5
0,5455 0,5 0,60,2727 0,25 0,20,1818 0,25 0,2
Lead t. WIP Setup1 0,55 0,24 0,21
Relative Weights
Normalised weights
F(x) = 0,55.||Lt(x)|| + 0,24.||WIP(x)|| + 0,21.||Set(x)||
Normalised criterion
To minimize
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Franck FONTANILI - CGI IMSM'07
Choice of the objective function
• Running a simulation
Proposed solution
Campaign to release
Assembly order
Finished product
referenceQuantity Load. WS 1 WS 2 WS 3 WS 4 WS 5 WS 6 Unload.
1 A 10 3 4 2 3 5
2 C 5 3 1 4 3 2 5
3 E 8 4 3 4 5 5
4 B 15 3 4 5
5 F 6 3 1 2 3 5
Objective function
Control parameters
IrTi(1) IrTi(2) IrTi(3) IrTi(4) IrTi(5)
9 9 5 5 2
StAm(1)StAm(2)StAm(3)StAm(4)StAm(5)StAm(6)
2 1 5 6 2 3
Rp
20
LeadTime WIP SetUp F(x)724,918 13,41 32 0,645
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Franck FONTANILI - CGI IMSM'07
Coupling Simulation with Optimization
Proposed solution
Simulation model
Optimization Algorithm
= Genetic Algorithm
Campaign to release
Control parameters
Algorithmparameters
Objective function
Why a Genetic Algorithm?•High-performance for complex problems
•Exploration of parallel solutions•Easy to program
From the algorithm (coded in Delphi)
Witness is an Object Linked Embedding
(OLE)
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Franck FONTANILI - CGI IMSM'07
Evolution and Genetic Algorithm
Proposed solution
Chromosome
GeneIndividualGeneration
Crossover
Mutation
Selection
Evaluation
For m generations For n individuals
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Franck FONTANILI - CGI IMSM'07
Coding our problem with GA
Proposed solution
Gene 1
IrTi(1) IrTi(2) IrTi(3) IrTi(4) IrTi(5)
Gene 2 Gene 3 Gene 4 Gene 5
StAm(1)StAm(2)StAm(3)StAm(4)StAm(5)StAm(6) Rp
Gene 6Gene 7Gene 8Gene 8Gene 10Gene 11Gene 12
a chromosome = a combination of control parameters
1- Evaluation
2- Elitist selection parent
#1
2- Elitist selection parent #2
IrTi(1) IrTi(2) IrTi(3) IrTi(4) IrTi(5) StAm(1)StAm(2)StAm(3)StAm(4)StAm(5)StAm(6) Rp LeadTime WIP SetUp F(x)2 7 11 5 6 4 6 5 4 3 2 24 695,212 14,45 37 0,633 15 6 10 2 4 4 3 3 1 3 3 33 657,152 19,05 40 0,696 28 9 10 12 3 6 3 2 1 5 3 28 758,946 13,89 21 0,68 39 9 5 5 2 2 1 5 6 2 3 20 724,918 13,41 32 0,645 48 4 7 8 5 5 1 5 5 4 4 30 629,772 17,8 44 0,615 52 12 8 10 9 5 1 4 3 1 4 25 701,466 15,98 56 0,798 69 2 1 6 7 2 3 3 3 5 5 29 541,246 17,8 41 0,387 71 9 6 2 10 4 1 3 6 3 3 33 655,946 19,36 55 0,785 811 7 12 10 9 1 1 2 2 5 4 21 700,332 13,5 32 0,589 99 2 1 6 7 2 3 3 3 5 5 29 541,246 17,8 41 0,387 111 7 12 10 9 1 1 2 2 5 4 21 700,332 13,5 32 0,589 29 2 1 6 9 1 1 2 2 5 4 21 698,266 14,07 42 0,656 311 7 12 10 7 2 3 3 3 5 5 29 718,346 13,73 24 0,594 49 7 12 10 9 1 1 2 2 5 4 21 676,726 13,77 27 0,513 511 2 1 6 7 2 3 3 3 5 5 29 604,172 17,93 40 0,536 69 2 1 6 7 2 3 3 3 5 4 21 724,452 13,91 31 0,653 711 7 12 10 9 1 1 2 2 5 5 30 672,166 14,41 32 0,548 86 8 5 4 8 4 5 2 2 3 5 25 593,712 15,41 28 0,369 96 8 5 4 8 4 5 2 2 3 5 25 593,712 15,41 28 0,369 19 2 1 6 7 2 3 3 3 5 5 29 541,246 17,8 41 0,387 2
3- Crossover (crossing
point)
4- Mutation (mutant)
For generations = 1 to 30For individual = 1 to
9
Next generation Next individual
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Franck FONTANILI - CGI IMSM'07
Running simulation and GA
Proposed solution
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Franck FONTANILI - CGI IMSM'07
Objective function
Results obtained by coupling simulation and GA
Genetic algorithm results
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
11 14 27 40 53 66 79 92 105
118
131
144
157
170
183
196
209
222
235
248
261
274
Iterations
Obj
ectiv
e fu
nctio
n
MovingAverageObj. funct.
min(Obj. fct.)
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Franck FONTANILI - CGI IMSM'07
Normalized criteria
Results obtained by coupling simulation and GA
Minimal values of the objective function and normalized criteria
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
1 21 41 61 81 101 121 141 161 181 201 221 241 261Iterations
Obj
. fun
ct.
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
Lead
T. /
WIP
/ S
etup
s
min(Obj. fct.)
Lead Time
WIP
Setup
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Franck FONTANILI - CGI IMSM'07
Best solution found by the GA
Results obtained by coupling simulation and GA
0,00
0,20
0,40
0,60
0,80
1,00
0,00 0,20 0,40 0,60 0,80 1,00
Lead Time
WIP
0,00
0,20
0,40
0,60
0,80
1,00
0,00 0,20 0,40 0,60 0,80 1,00
Setup
WIP
0,00
0,20
0,40
0,60
0,80
1,00
0,00 0,20 0,40 0,60 0,80 1,00Lead Time
Set
up
The best solution is (at the 264th iteration after 5 minutes) :
IrTi(1) IrTi(2) IrTi(3) IrTi(4) IrTi(5) StAm(1)StAm(2)StAm(3)StAm(4)StAm(5)StAm(6) Rp LeadTime WIP SetUp F(x)6 9 5 9 8 6 5 5 4 3 3 22 552 13.6 22 0,072
Best of WIP
Best of Setup
Best of Lead Time
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Franck FONTANILI - CGI IMSM'07
Conclusions
• GA finds a « good » solution in less than 5 minutes allowing its use during the preparation time (idle time)
• Simulation coupled with GA provides a decision-making aid to the manager.
• Take into account other parameters: sequencing and orders splitting
• Take into account other constraints : scheduling on each workstation
Conclusions and perspectives
Perspectives