CrewGroups Recent Development and Plans for the Future

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CrewGroupsRecent Development and Plans for the
Future

• Presentation at SweConsNet03
• Tomas Lidén
• Carmen Consulting AB
• tomas.liden_at_carmenconsulting.com

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Outline

• Introduction
• Constraints and costs
• Program flow, search algorithm
• Discussion, future plans

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Background

• Normal scheduling (rostering)
• - Each flight has different crew
• Greater flexibility
• Group scheduling (rostering)
• Same crew fly together for a month
• - Less flexibility

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CrewGroups on One Page

• Problem Construct homogenous groups (flight
  cabin crew)
• Characteristics Assignment, non-additive costs
• Developed during 2001 for IberiaIn production
  since spring 2002Further developed regarding
  December functionality in fall 2002
• Currently a CP application using ILOG Solver with
  set variables, one customized constraint, global
  local search
• Thesis work on alternative techniques. Column
  generation yields better performance and slightly
  better solution quality. Porting currently
  discussed (without CP).

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Structure
Group
Days handled with set variables. Historic values
handled with integer variables. Cost and
constraints applied on the above
variables. Normally construct min nr of groups,
but in December construct all possible
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Assignment Constraints

• Crew in buddy bid always assigned to a group
• Crew in buddy bid always kept together
• Exception in December
• Do not combine certain crew (anti bids)

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Simple Constraints

• Max nr of inexperienced per group
• Max nr of crew in transition course
• etc

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Handling of Days

• Consider size? Normally no December yes
• Constraint for max nr of days off
• Pattern constraint for days off ( _ _ _ x..x _ _
  _ )
• Analogue handling of days with preassigned duties

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Handling of Historic Values

• Size always considered

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Handling of Work Reduction

• Size not considered
• Never higher than the purser (constraint)

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Special handling in December - 1

• Day 32 (Jan 1st) considered for fairness work
  over Christmas and New Years Eve.
• Buddy bids split due to day 32
• Much lower cost if split bids are rejoined in
  same group ( X Y )

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Special handling in December - 2
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Program flow - Solve problem
Add hard constraints and find solution
Add/remove all additional constraints and find
solution
Global search for cheaper solution
Local search for cheaper solution
Print and analyze results
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Search heuristic, Global search

• Select a group (variable)
• Already used and buddy bids
• Factor x affecting difficulty and cost
• Select a subgroup (value) to assign
• Size and buddy bids
• Factor y affecting difficulty and cost

• Depth first
• Many factors to consider
• tradeoff between low cost (quality) and
  difficulty (solvability)
• Each new factor affects the search algorithm!
• Not clear how sensible algorithm is for different
  weights

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More problems in December

• All groups must be produced longer execution
  times.
• Special search algorithm needed!
• Handling of rejoined bids hard. Too greedy search
  will not find possible solutions. Ungreedy search
  will miss good rejoinings (worse solution
  quality)
• A pure CP application should have a better local
  search. Tabu?

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Column generation

• Benefits
• faster (4-6 times for large problems)
• better (5-10 lower cost, even more in December)
• more stable (less sensitive for weights and new
  factors)
• CP not needed for generation
• Constraints column legality
• Cost straightforward to calculate
• Domain reduction (for quicker generation) can
  easily be implemented
• Porting/rewriting considered

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Discussion, CP suitable or not?

• Initial arguments
• tricky constraints
• non-additive, non-linear cost
• unclear problem
• few possible solutions
• Current opinion
• Works ok, but not the best
• ColGen better, hybrid solver perhaps optimal
• Challenging problem for CPlocal search?

Yes, good during modelling and development
No!
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• END
• Thank you for your attention!
• Questions?