AGIFORS, 5/28/03 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

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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)

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 4 Current Practice aircraft routing crew pairing Crew sit connection less than the minimum sit connection time only if crew stays on the same aircraft.

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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?

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 7 Assumptions Hub-and-spoke network The aircraft routing problem is merely a feasibility problem. –No objective

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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.

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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.

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 10 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. 8:00 8:15 8:16 8: How to prevent such a selection?

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 11 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

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 12 Plane count constraints: for all. Constraints Cover each leg by a pairing:

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 14 Example :00 20:00 12:00 12:40 pairings covering flights 1 and 4

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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 …- ….).

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 16 Computation Experiments Cluster of PCs (extremely cheap) Execution times comparable to traditional crew pairing approaches.

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 17 Results-FTC

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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.

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 20 Business Processes Changes to business processes? Bridging the gap between two separate groups (typically)

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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.

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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.

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 23 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 min Minimum sit time = 45 min

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 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.

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 25 Results-FTC w = window size

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 26 Major Flaw Where are the passengers? –Changed departure times disrupt passenger connections. Who cares about passengers! This is the crew management study group!

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 27 Major To-Do Project Incorporate PAX to the time windows approach Integrated planning –Fleeting (PAX on the horizon) –Aircraft routing –Crew pairing OR

Aircraft Routing and Crew Pairing Optimization AGIFORS crew management study group 28