1 franck fontanili - cgi imsm'07 content of the presentation introduction and context problem...

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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

2


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

3


Manufacturing system

• Free automated transfer with belt conveyors

• Manual or automated assembly operations• Workstations layout in: series or parallel


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

4


Flow of pallets


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

5


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

6


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

7


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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• 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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• 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 ?

10


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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Use of Simulation

• Simulation of a k order campaign on j workstations

Proposed solution

Campaign to release

Assembly order

Finished product


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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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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Choice of the objective function

• Running a simulation

Proposed solution

Campaign to release

Assembly order

Finished product


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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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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Evolution and Genetic Algorithm

Proposed solution

Chromosome

GeneIndividualGeneration

Crossover

Mutation

Selection

Evaluation

For m generations For n individuals

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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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Running simulation and GA

Proposed solution

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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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Normalized criteria


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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Best solution found by the 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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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

1 franck fontanili - cgi imsm'07 content of the presentation introduction and context problem...

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