Stochastic Maintenance Scheduling Problem

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Stochastic Maintenance Scheduling Problem

• G. Fleury, P. Lacomme,
• M. Sevaux

Laboratoire dInformatique Clermont-Ferrand UMR
6158
Laboratoire de Mathématiques Clermont-Ferrand UMR
6620
LAMIH Valenciennes UMR 8530
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Plan

• Problem statement
• Assumptions and objective
• Genetic Algorithm template
• Computational experiments
• Future research

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Problem statement
10 000 elementary tasks
8 majors operations for each coach
64 aggregated tasks for one TGV
Objective minimize the total duration
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Physical description (1)
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Physical description (2)

• CTAx (caisses TGV et Automoteur)
• Dis-assembling tasks
• Re-assembling tasks
• Works insided coaches
• IP (industries privées)
• Sand blasting by external companies
• TSCx (tôlerie, stucture de caisse)
• Handling the tollery
• Renovation of external parts of coaches

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Logical description (1)
jobs sequence of treatment
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Logical description (2)
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A stochastic problem (1)

• Processing time of jobs are submitted to
  variations
• Robust solutions are required to avoid periodic
  computation of new schedule
• Minimization of the makespan is also required

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Random events modelization

• ? extra delay
• pp probability of random events occurrences

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A template for stochastic problem (1)
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A template for stochastic problem (2)

• Optimization phase
• Searching process based of statistic
  performances of solutions
• Robustness evaluation of solutions
• Replications
• Average cost of solution
• Standard deviation of solutions

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Genetic Algorithm template (1)

• Construct a random initial set of solutions
• Repeat
• Select P1 and P2 based on the inverse function
  of the fitness rank distribution
• Apply XOver operator
• Evaluate C
• With probability P then
• Mutate C (swap two random points p and q)
• Until (a maximal number of iterations is
  reached).
• ? See (Sevaux and Le Quéré, 2003)

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Genetic Algorithm template (2)

• One chromosome is
• Ordered set of jobs
• Evaluation of the average cost
• Evaluation of the standard deviation cost

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Robust Approach

• Principles
• Compute
• which is a evaluation of the average cost over n
  replications
• Compute
• which is evaluation of the standard deviation
  over n replications
• Problems
• Very costly for a computational point of view

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Stochastic Approach (1)

• Replace statistical evaluation by mathematical
  evaluation
• Based on shortest path computed in the
  disjunctive graph

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Stochastic Approach (2)

• Tasks duration
• ? with
• ?
• ? ? Y binomial law

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Stochastic Approach (3)

• So
• Average
• Standard deviation
• Finally

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Results for the robust approach
(Sevaux and Le Quéré, 2003)
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Results for the robust approach
Results with mathematical evaluation of criteria
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Concluding remarks (1)

• Stochastic maintenance problem
• Two approaches
• A robust approach
• A stochastic approach
• Both approaches provides robust solutions

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Concluding remarks (2)

• Robust Approach
• High quality solutions
• Post analysis provide results very closed to the
  evaluations
• Time consuming
• Stochastic Approach
• Satisfactory evaluation of soluitons
• Very short computational time

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Future Research

• Improve mathematical analysis
• ? Take into account all shortest paths
• Improve modelization of the problem
• ? modelize random variations