Boarding at the Speed of Flight 2007 MCM Problem B Paper by Bauer, Bhawalkar, Edwards Duke University Presentation by Edward Ly

Modeling Objectives To minimize the overall boarding (and de- boarding) time. Judging a Model: – Boarding Efficiency – Passenger satisfaction – Feasibility

Modeling Assumptions Special-needs and first-class passengers are not considered. Every passenger in the model is on-time for boarding. Every passenger walks at the same speed when boarding. Every seat is occupied by a passenger. There is enough room in the plane for all carry-on luggage. If seats are assigned, each person sits in their assigned seats. The airplane in our model has one aisle and entrance with three seats per row on each side of the aisle.

Variables C: the number of columns in the plane, or the number of seats in a row. R: the number of rows in the plane, assumed to be equally spaced out. B: the time for a person to stow luggage. v: the walking speed of passengers, assumed to be constant. s: the time for an already-seated passenger to get up and get out into the aisle to let another passenger pass. λ: the rate at which people enter the plane through the main door.

Order of Passengers? If seats are assigned: – Individual location in row: Window has highest priority, aisle has least. – Side of plane: left side of plane has priority over right side. – Row number: Rows in back have priority over those in front. Random Order? Stochastic Simulation

Queuing Theory

Ranking Boarding Schemes Outstanding: No assigned seats Meritorious: Outside-in, reverse-pyramid, parabola Honorable Mention: Alternating rows Limited Success: Back-to-front

Conclusion Minimizing the time to stow baggage is critical to the overall boarding time. Maximizing the rate at which passengers check-in at the gate is critical. Random boarding without assigned seats consistently produces the fastest boarding times, but often leads to low customer satisfaction.