MCM: The Mathematical Contest in Modeling
ICM: The Interdisciplinary Contest in Modeling
2002 Mathematical Contest in Modeling
The Problems
Problem A
Authors: Tjalling Ypma
Title: Wind and Waterspray
An ornamental fountain in a large open plaza surrounded by buildings
squirts water high into the air. On gusty days, the wind blows
spray from the fountain onto passersby. The water-flow from
the fountain is controlled by a mechanism linked to an anemometer
(which measures wind speed and direction) located on top of
an adjacent building. The objective of this control is to provide
passersby with an acceptable balance between an attractive spectacle
and a soaking: The harder the wind blows, the lower the water
volume and height to which the water is squirted, hence the
less spray falls outside the pool area.
Your task is to devise an algorithm which uses data provided
by the anemometer to adjust the water-flow from the fountain
as the wind conditions change.
Problem B
Authors: Bill Fox and Rich West
Title: Airline Overbooking
You're all packed and ready to go on a trip to visit your
best friend in New York City. After you check in at the ticket
counter, the airline clerk announces that your flight has
been overbooked. Passengers need to check in immediately to
determine if they still have a seat.
Historically, airlines know that only a certain percentage of
passengers who have made reservations on a particular flight
will actually take that flight. Consequently, most airlines
overbook-that is, they take more reservations than the capacity
of the aircraft. Occasionally, more passengers will want to
take a flight than the capacity of the plane leading to one
or more passengers being bumped and thus unable to take the
flight for which they had reservations.
Airlines deal with bumped passengers in various ways. Some
are given nothing, some are booked on later flights on other
airlines, and some are given some kind of cash or airline ticket
incentive.
Consider the overbooking issue in light of the current situation:
Less flights by airlines from point A to point B
Heightened security at and around airports
Passengers' fear
Loss of billions of dollars in revenue by airlines to date
Build a mathematical model that examines the effects that different
overbooking schemes have on the revenue received by an airline
company in order to find an optimal overbooking strategy, i.e.,
the number of people by which an airline should overbook a particular
flight so that the company's revenue is maximized. Insure that
your model reflects the issues above, and consider alternatives
for handling "bumped" passengers. Additionally, write
a short memorandum to the airline's CEO summarizing your findings
and analysis.
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