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Optimizing Airline Operations with Linear Programming: A Pilot's Guide

This overview explores the complexities of airline operations, highlighting the significant impact of linear programming techniques in scheduling aircraft, crew management, and sales strategies. With hundreds of aircraft and thousands of crew members, the industry faces daunting challenges, including scheduling up to 100,000 flights monthly. Notable results, including cost reductions and improved revenue, demonstrate the potential of these mathematical models. We also discuss real-world implementations, highlighting the gains made by major airlines through effective scheduling and resource allocation.

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Optimizing Airline Operations with Linear Programming: A Pilot's Guide

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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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