agifors, 5/28/03 aircraft routing and crew pairing optimization diego klabjan, university of...

AGIFORS, 5/28/03

Aircraft Routing and Crew Pairing Optimization

Diego Klabjan, University of Illinois at Urbana-Champaign

George L. Nemhauser, Georgia Institute of TechnologyEllis L. Johnson, Georgia Institute of Technology

Funded by United Airlines

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Aircraft Routing andCrew Pairing Optimization

AGIFORScrew

managementstudy group

Aircraft Routing

• Assign a tail number to each flight in the schedule.

• Constraints– Preserve the plain count– Maintenance feasibility– Big cycle constraint

• Objective– Primarily a feasibility problem– Throughs

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Crew Pairing

• Given a flight schedule, find the least collection of pairings

• Very difficult to solve for large fleets

• Constraints– Pairing feasibility rules– Cover each flight– Side constraints

• Objective– Crew cost– (Robustness)

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Current Practice

aircraft routing

crew pairing

Crew sit connection less than

the minimum sit connection time only if

crew stays on the same aircraft.

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Integration

• Aircraft routing is an input to crew pairing. • Integrate aircraft routing and crew pairing.• Main idea

–Solve first the crew pairing problem.• Any connection longer than the

minimum plane turn time is considered.

–Some pairings imply plane turns. • Can these plane turns be extended to

aircraft routes?

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Integration

• No!

• The plane count is violated.• We add constraints to crew pairing

guaranteeing that plane count feasible routes can be obtained.

• On hub-and-spoke networks– Maintenance feasibility not a problem– Big cycle not a problem

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Assumptions

• Hub-and-spoke network

• The aircraft routing problem is merely a feasibility problem.– No objective

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Aircraft Routing and Crew Pairing

• Traditional approach– Solve the aircraft routing problem.– Solve the crew pairing problem.

• Our approach– First solve crew pairing.– Solve aircraft routing.

• Embed plane count constraints into the crew pairing model.

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Basic Concept

• An optimal solution to FAM is given.– At any point in time and at any station the

number of planes on the ground is given.

• Consider also pairings that have sit connections shorter than the minimum sit connection time but longer than the minimum plane turn time.

• Some pairings imply plane turns.

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Example

• If flights 1 and 4 are in the same pairing, then the plane count between flights 2 and 3 is 1.

• However the ground arc value is 0. • We have to forbid such pairings.

8:008:15

8:16

8:311

2

3

4

How to prevent such a selection?

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Notation

• For each define to be the set of all the pairings having a sit connection that ‘includes’ the time interval spanned by g and the time of the sit connection in question is shorter than the minimum sit connection time.

less than min sit minutes

ground arc g

pairing

Gg gP

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• Plane count constraints:

for all .

Constraints

• Cover each leg by a pairing:

g

gPpp by

Gg

1 py

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Redundant Constraints

• It can be seen that the only plane count constraints that are needed are those corresponding to ground arcs being present in the FAM model.

• This reduces the number of plane count constraints considerably.

no activity

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Example

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1 2 3

54 6

26,35,34,36,25,24,26,15,14,1 yyyyyyyyy

8:0020:00

12:0012:40

4,1y pairings covering flights 1 and 4

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New Approach

• Solve the crew pairing problem with plane count constraints.

• The solution implies some plane turns.

• Extend these plane turns into an aircraft rotation.– Definitely possible to satisfy the plane count

constraint.– If you cannot extend, give me a call (217 …-

….).

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Computation Experiments

• Cluster of PCs (extremely cheap)

• Execution times comparable to traditional crew pairing approaches.

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Results-FTC

No. legs

Traditional CP

Integrated approach

119 3.94% 2.21%

190 3.12% 1.85%

342 2.86% 1.40%

449 0.31% 0.08%

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Number of Used Plane Turns

• What about the wisdom:– Crew should follow the

aircraft as often as possible!

• A second benefit of the integrated approach

No. legs

Traditional CP

Integrated approach

119 2 9

190 11 11

342 17 59

449 66 142

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Should I be Using it?

• A very simple concept– Even though it requires a new perspective.

• Only a minor change to the crew pairing solver.

• When not to use it?– Only a few feasible solutions to the routing

problem– We badly want to obtain the maximum revenue

routes.

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Business Processes

• Changes to business processes?

• Bridging the gap between two separate groups (typically)

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The Story Since

• United was using this approach (perhaps still in production).

• Carmen Systems uses a variant.

• Academia– Cordeau et. al. (2002) present a fully

integrated model.– Cohn, Barnhart (2003) generate several routes

and allow only plane turns from these routes.

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Time Windows

• Integration of crew pairing and schedule planning

• Each departure time has a time window.

• Find pairings and new departure times such that the pairings are feasible based on the retimed schedule.

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Capture New Pairings

• Pairings which are infeasible based on the original flight schedule may become feasible for a retimed schedule.

35 min

45 min

Window size = 5 minMinimum sit time = 45 min

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Time Windows

• New pairings– Substantial gains

• Cost of a pairing might decrease– Very minor gain, neglected

• Methodology– Generate new departure times and pairings

simultaneously.– We do not discretize the time.

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Results-FTC

Num. legs

CS w=0 w=5 w=10

119 3.94% 2.21% 1.71% 1.35%

190 3.12% 1.85% 1.54% 1.06%

342 2.86% 1.40% 0.88% 0.88%

449 0.31% 0.08% 0.08% 0.08%

w = window size

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Major Flaw

• Where are the passengers?– Changed departure times disrupt passenger

connections.

• Who cares about passengers! This is the crew management study group!

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Major To-Do Project

• Incorporate PAX to the time windows approach

• Integrated planning– Fleeting (PAX on the

horizon)– Aircraft routing– Crew pairing

OR

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agifors, 5/28/03 aircraft routing and crew pairing optimization diego klabjan, university of...

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