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% • 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

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

Fleet Assignment

• Right size for the lane to maximize profits

• Marketing projections• Rotate aircraft to meet maintenance

requirements

Crew Scheduling

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

Crew Rules

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

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

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!

Advertising at NBC?

$50m revenue increase

Finance - Capital Asset Pricing Model (CAPM)

• Find the efficient frontier