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 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

Cement Inputs Inputs from different sources, different amounts of several different compounds Target levels of each in finished product Transportation costs complicate

Summary Linear Programming widely used Airlines have saved and earned billions because of LP So much so, you never read about it Advertising at NBC - $50m in revenues Capital Asset Pricing model Cement raw materials purchasing