Aircraft Routing and Crew Pairing Optimization

1. Aircraft Routing and Crew Pairing Optimization Diego Klabjan, University of Illinois at Urbana-Champaign George L. Nemhauser, Georgia Institute of Technology Ellis L. Johnson, Georgia Institute of Technology Funded by United Airlines

2. 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. 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. Current Practice aircraft routing Crew sit connection less than the minimum sit connection time only if crew stays on the same aircraft. crew pairing

5. 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. 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. Assumptions • Hub-and-spoke network • The aircraft routing problem is merely a feasibility problem. • No objective

8. 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. 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. 2 4 8:16 8:00 8:15 8:31 1 3 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. How to prevent such a selection?

11. pairing ground arc g less than min sit minutes 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.

12. Plane count constraints: for all . Cover each leg by a pairing: Constraints

13. 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. Example 5 6 4 8:00 12:00 2 12:40 20:00 1 2 3 pairings covering flights 1 and 4

15. 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. Computation Experiments • Cluster of PCs (extremely cheap) • Execution times comparable to traditional crew pairing approaches.

17. Results-FTC

18. 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

19. 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. Business Processes • Changes to business processes? • Bridging the gap between two separate groups (typically)

21. 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. 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. 45 min 35 min Window size = 5 min Minimum sit time = 45 min Capture New Pairings • Pairings which are infeasible based on the original flight schedule may become feasible for a retimed schedule.

24. 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. Results-FTC w = window size

26. Major Flaw • Where are the passengers? • Changed departure times disrupt passenger connections. • Who cares about passengers! This is the crew management study group!

27. Incorporate PAX to the time windows approach Integrated planning Fleeting (PAX on the horizon) Aircraft routing Crew pairing Major To-Do Project OR

28. Thank you for your attention!