1. Airlines and Linear Programming Dr. Ron Tibben-Lembke

2. Complex Problems Several hundred aircraft 10,000+ crew members Up to 100,000 flights per month Tens of millions of passengers per year

3. A Few Results 1989: American Airlines Reduced costs by 0.5% Increased revenues by 0.5% Total impact ~ $75m 1994: PanAm 11% reduction in labor 1993: Delta – Fleet Assignment $300m in 3 years 1% difference in solution quality can mean $30m in annual savings

4. Schedule Design Which cities to fly to when, how often, what times? Marketing estimates demand Consider available fleets, constraints on network Gates available, airport capacity, timing

5. Fleet Assignment Right size for the lane to maximize profits Marketing projections Rotate aircraft to meet maintenance requirements

6. Crew Scheduling

7. Crew pairing Which flight legs are combined in rotations Fly so many hours over a period of so many hours Different national rules, unions Quality of life: Rest days at home, days on the road, etc. Crew-rostering Trips are assigned to individuals SAS: 1% improvement saves $5m per year

8. Crew Rules

9. Operations Control Dealing with disruptions: Weather delays, rain, snow, wind Mechanical issues Flight crews timed out Getting the network back up and running as quickly as possible, Trying to service as many travelers as possible

10. The Bad News Fleet Assignment: 75,000 Binary variables 1,000 integer variables 50,000 constraints Produce a solution within a day of getting the data

11. Crew Flight Scheduling In fact, for most real instances, explicit enumeration of the constraint matrix is not possible. For example, a domestic problem on a hub-and-spoke network with several hundred flights typically has billions of pairings. You can’t even write all of the constraints!