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Airlines and Linear Programming (and other stuff)

Airlines and Linear Programming (and other stuff). Dr. Ron Lembke. Complex Problems. Several hundred aircraft 10,000+ crew members Up to 100,000 flights per month Tens of millions of passengers per year. A Few Results. 1989: American Airlines Reduced costs by 0.5%

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Airlines and Linear Programming (and other stuff)

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  1. Airlines and Linear Programming (and other stuff) Dr. Ron 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 Scheduling • 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!

  12. Advertising at NBC?

  13. $50m revenue increase

  14. Finance - Capital Asset Pricing Model (CAPM) • Find the efficient frontier

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