stochastic maintenance scheduling problem
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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
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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)
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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
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A template for stochastic A template for stochastic problem (1)problem (1)
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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)
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Results for the robust approachResults for the robust approachResults with mathematical evaluation of criteriaResults with mathematical evaluation of criteria
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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
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