Solving Large Scale Crew Scheduling Problems by using Iterative Partitioning

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Solving Large Scale Crew Scheduling Problems by
using Iterative Partitioning
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Contents

• Introduction CSP at NS
• Problem formulation
• Background applying partitioning
• Results

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Dutch Railway System

• Dense railway system
• Cyclic timetable (1 hr)
• High utilization of infra
• Over 5000 trains per day
• Over 1 million passengers per day

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Crew planning at NS
Huisman et al. (2005), Operations Research in
passenger railway transportation, Stat.
Neerlandica 59, 467-497
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Crew scheduling at NS

• 3000 train drivers
• 3500 conductors
• 29 depots
• Duties are created in Ut
• Rosters are created
• locally in the depots

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Duty rules
Minimum transfer time
Pre- and post times
Meal break rule

• - Route knowledge
• Rolling stock knowledge

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Global Rules
Maximum percentage night duties
Maximum average duty length
Maximum percentage long duties (gt9 hrs)
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Aggression Train
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Sharing SweetSour

• Additional variation rules
• Max percentage of aggression work per depot
• Max standard deviation on aggression
• Max Repetitions In Duties (RID)
• Min percentage of preferred trains per depot
• Max standard deviation on preferred trains
• Min number of routes per depot
• Min average number of routes
• Max percentage of Rolling Stock cluster per depot

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Aggression trains (2)
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Mathematical Formulation

• Formulated as set covering problem with
• xk 1 if duty k is selected and 0 otherwise

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Solution approach

• Main problem in solving CSP enormous amount of
  potential duties (columns)
• Solution apply column generation techniques!
• Currently, NS uses TURNI (Double Click sas)to
  solve CSP from scratch
• TURNI is an algorithm based on column generation
  and Lagrangian heuristics and uses
  intensification through variable fixing / local
  branching

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The TURNI Machine
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CSP Instances at NS
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Initial Working Method with TURNI

• We planned 3 separate days with TURNIa pattern
  Weekday, a Saturday and a Sunday
• Planners fine-tuned the overall plan

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Notions

• Running a small instance of the large one
  sometimes gives an improved solution
• Planners are able to improve the solution by a
  few percentages, possibly due to- Missing
  positioning trips- Slack in global constraints-
  The large instances are too complex

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Idea

• Refine solution after running the initial case
• Try to run partial cases for the complete week

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Illustration
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Partitioning methods

• Weekday
• Geographical region (large and small)
• Train line based
• Column info

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Depot Cluster Methods

• Based on
• Geographical location
• Train line connections
• Size of depots

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Column Info Method
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New Working Method

• Fully automated partitioning process.
• Iterative (parallel) optimization of several
  sub-sets
• Per day (3 runs of about 12 Hours)
• Per region (4 runs of about 6 Hours)
• Per sub-region (12 runs of about 2 hours)
• Per line partition (4 runs of about 6 Hours)
• Solution and columns are passed to next instance

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Results, All Constraints
Guards, all constraints, week optimization Dri
vers, all constraints, day optimization
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Results, No Capacity Constraints

• Drivers, Different average per day (max 740
  week, 915 weekend)
• Drivers, Average 800 for every day, No capacity
  constraints

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Results

• Optimizing over the week gives excellent
  results2-4 efficiency equals 120-240 FTE
  reduction
• Partitioning based on column info indicates
  possibility to fully partition based on series.

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