airlines and linear programming (and other stuff)
DESCRIPTION
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% - PowerPoint PPT PresentationTRANSCRIPT
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
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