A: Design of an Airline Terminal
The design of airline terminals varies widely.
The sketches below show airline terminals from several cities. The designs are quite dissimilar. Some involve circular
arcs; others are rectangular; some are quite irregular.
Which is optimal for operations? Develop a mathematical
model for airport design and operation. Use your model
to argue for the optimality of your specified design. Explain
how it would operate.
B: Forest Service
Your team has been approached by the Forest
Service to help allocate resources to fight wildfires.
In particular, the Forest Service is concerned
about wildfires in a wilderness area consisting of small
trees and brush in a park shaped like a square with dimensions
80 km on a side. Several years ago, the Forest Service
constructed a network of north-south and east-west firebreaks
that form a rectangular grid across the interior of the
entire wilderness area. The firebreaks were built at 5
Wildfires are most likely to occur during
the dry season, which extends from July through September
in this particular region. During this season, there is
a prevailing westerly wind throughout the day. There are
frequent lightning bursts that cause wildfires.
The Forest Service wants to deploy four
fire-fighting units to control fires during the next dry
season. Each unit consists of 10 firefighters, one pickup
truck, one dump truck, one water truck (50,000 liters),
and one bulldozer (w/ truck and trailer). The unit has
chainsaws, hand tools, and other fire-fighting equipment. The people can be quickly moved by helicopter within the
wilderness area, but all the equipment must be driven via
the existing firebreaks. One helicopter is on standby at
all times throughout
the dry season.
Your task is to determine the best distribution
of fire-fighting units within the wilderness area. The
Forest Service is able to set up base camps for those units
at sites anywhere within the area. In addition, you are
asked to prepare a damage assessment forecast. This forecast
will be used to estimate the amount of wilderness likely
to be burned by fire as well as acting as a mechanism for
helping the Service determine when additional fire-fighting
units need to be brought in from elsewhere.