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Stochastic Maintenance Stochastic Maintenance Scheduling ProblemScheduling Problem

G. Fleury, P. Lacomme, G. Fleury, P. Lacomme,

M. SevauxM. Sevaux

Laboratoire Laboratoire d’Informatiqued’Informatique

Clermont-Ferrand Clermont-Ferrand UMR 6158UMR 6158

Laboratoire de Laboratoire de MathématiquesMathématiques

Clermont-Ferrand Clermont-Ferrand UMR 6620UMR 6620

LAMIHLAMIH

ValenciennesValenciennes

UMR 8530UMR 8530

22

PlanPlan

Problem statementProblem statement Assumptions and objectiveAssumptions and objective Genetic Algorithm templateGenetic Algorithm template Computational experimentsComputational experiments Future researchFuture research

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Problem statementProblem statement

Maintenance

10 000 elementary tasks10 000 elementary tasks

8 majors operations for each coach8 majors operations for each coach

64 aggregated tasks for one TGV64 aggregated tasks for one TGV

Objective:Objective: minimize the total minimize the total durationduration

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Physical description (1)Physical description (1)

CTA1

CTA2

CTA3

CTA4

IP

TSC1

TSC2

coaches 1, 2

coaches 3, 4

coaches 5, 6

coaches 7, 8

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Physical description (2)Physical description (2)

CTAx CTAx (caisses TGV et Automoteur):(caisses TGV et Automoteur):

Dis-assembling tasksDis-assembling tasks

Re-assembling tasksRe-assembling tasks

Works insided coachesWorks insided coaches

IPIP (industries privées):(industries privées):

Sand blasting by external companiesSand blasting by external companies

TSCx TSCx (tôlerie, stucture de caisse):(tôlerie, stucture de caisse):

Handling the tolleryHandling the tollery

Renovation of external parts of coachesRenovation of external parts of coaches

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Logical description (1)Logical description (1)

jobs sequence of treatmentjobs sequence of treatment

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Logical description (2)Logical description (2)

88

A stochastic problem (1)A stochastic problem (1)

Processing time of jobs are Processing time of jobs are submitted to variationssubmitted to variations

Robust solutions are required to Robust solutions are required to avoid periodic computation of new avoid periodic computation of new scheduleschedule

Minimization of the makespan is also Minimization of the makespan is also requiredrequired

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Random events modelizationRandom events modelization

: extra delay: extra delay

pppp : probability of random events : probability of random events occurrences occurrences

1010

A template for stochastic A template for stochastic problem (1)problem (1)

1111

A template for stochastic A template for stochastic problem (2)problem (2)

Optimization phase: Optimization phase: Searching process based of statistic Searching process based of statistic

performances of solutionsperformances of solutions

Robustness evaluation of solutionsRobustness evaluation of solutions ReplicationsReplications Average cost of solutionAverage cost of solution Standard deviation of solutionsStandard deviation of solutions

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Genetic Algorithm template (1)Genetic Algorithm template (1)

Construct a random initial set of solutionsConstruct a random initial set of solutionsRepeatRepeat Select Select P1P1 and and P2P2 based on the based on the inverse function of inverse function of

the fitness rank distributionthe fitness rank distribution Apply Apply XOverXOver operator operator

Evaluate Evaluate CCWith probability With probability PP then then

Mutate Mutate C C (swap (swap two random points two random points pp and and qq)) UntilUntil (a maximal number of iterations is reached). (a maximal number of iterations is reached).

See See (Sevaux and Le Quéré, 2003)(Sevaux and Le Quéré, 2003)

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Genetic Algorithm template (2)Genetic Algorithm template (2)

One chromosome is:One chromosome is:

– Ordered set of jobsOrdered set of jobs

– Evaluation of the average costEvaluation of the average cost

– Evaluation of the standard deviation costEvaluation of the standard deviation cost

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Robust ApproachRobust Approach

PrinciplesPrinciples ComputeCompute

which is a evaluation of the average cost over which is a evaluation of the average cost over nn replicationsreplications

ComputeCompute

which is evaluation of the standard deviation over which is evaluation of the standard deviation over nn replicationsreplications

ProblemsProblemsVery costly for a computational point of viewVery costly for a computational point of view

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Stochastic Approach (1)Stochastic Approach (1)

Replace statistical evaluation by Replace statistical evaluation by mathematical evaluationmathematical evaluation

Based on shortest path computed in Based on shortest path computed in the disjunctive graphthe disjunctive graph

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Stochastic Approach (2)Stochastic Approach (2)

Tasks durationTasks duration

with with

YY binomial law binomial law

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Stochastic Approach (3)Stochastic Approach (3)

SoSo

Average : Average :

Standard deviation :Standard deviation :

Finally: Finally:

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Results for the robust approachResults for the robust approach(Sevaux and Le Quéré, 2003)(Sevaux and Le Quéré, 2003)

1919

Results for the robust approachResults for the robust approachResults with mathematical evaluation of criteriaResults with mathematical evaluation of criteria

2020

Concluding remarks (1)Concluding remarks (1)

Stochastic maintenance problemStochastic maintenance problem

Two approaches:Two approaches:A robust approachA robust approach

A stochastic approachA stochastic approach

Both approaches provides robust Both approaches provides robust solutionssolutions

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ConcludingConcluding remarks (2) remarks (2)

Robust ApproachRobust ApproachHigh quality solutionsHigh quality solutions

Post analysis provide results very closed to the Post analysis provide results very closed to the evaluationsevaluations

Time consumingTime consuming

Stochastic ApproachStochastic ApproachSatisfactory evaluation of soluitonsSatisfactory evaluation of soluitons

Very short computational timeVery short computational time

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Future ResearchFuture Research

Improve mathematical analysisImprove mathematical analysis Take into account all shortest pathsTake into account all shortest paths

Improve modelization of the problemImprove modelization of the problem modelize random variationsmodelize random variations