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Transcript of 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
2
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
3
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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)
4
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
Current Practice
aircraft routing
crew pairing
Crew sit connection less than
the minimum sit connection time only if
crew stays on the same aircraft.
5
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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?
6
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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
7
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
Assumptions
• Hub-and-spoke network
• The aircraft routing problem is merely a feasibility problem.– No objective
8
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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.
9
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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.
10
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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?
11
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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
12
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
• Plane count constraints:
for all .
Constraints
• Cover each leg by a pairing:
g
gPpp by
Gg
1 py
13
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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
14
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
Example
2
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
15
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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 …-
….).
16
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
Computation Experiments
• Cluster of PCs (extremely cheap)
• Execution times comparable to traditional crew pairing approaches.
17
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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%
18
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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
19
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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.
20
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
Business Processes
• Changes to business processes?
• Bridging the gap between two separate groups (typically)
21
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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.
22
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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.
23
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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
24
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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.
25
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
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
26
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
Major Flaw
• Where are the passengers?– Changed departure times disrupt passenger
connections.
• Who cares about passengers! This is the crew management study group!
27
Aircraft Routing andCrew Pairing Optimization
AGIFORScrew
managementstudy group
Major To-Do Project
• Incorporate PAX to the time windows approach
• Integrated planning– Fleeting (PAX on the
horizon)– Aircraft routing– Crew pairing
OR