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Best schedule to utilize the Big Long River
1 Introduction
People enjoy going to the Big Long River for its scenic views and exciting white water
rapids, and the only way to achieve this should be to take a river trip that requires
several days of camping, since the river is inaccessible to hikers. So far the rise in
popularity of river rafting has made it imminent for the park managers to look for a
better way to utilize the river in terms of its traveling value. In other words, there is a
need for an optimal schedule to use all the campsites on the river. However, this is
not an easy question when taking in account of tourists’ requirements for a
wilderness experience. Specifically, a basic rule for the arrangement of the river trips
should be that no two sets of campers could occupy the same campsite at the same
time in order to guarantee tourists minimal contact with other groups of tourists.
As given in the problem set, X river trips are currently available each year during a six
month period (the rest of the year it is too cold) on the Big Long River. All river trips
start at First Launch and exit at Final Exit, 225 miles downstream. There are Y
campsites on the river, distributed approximately uniformly throughout the river
corridor. The trips differ in mainly two aspects. The first is the ship propulsion, with
either oar-powered rubber rafts (average 4 mph) or motorized boats (average 8 mph).
The second is the trip duration, ranging from 6 days to 18 days. What we are
supposed to accomplish are to develop the best schedule and to determine the
carrying capacity of the river.
We have examined many policies for different river trips (including Grand Canyon in
Arizona, the U.S., Wolf River in Winconsin, the U.S., and Missinaibi river in Canada)
and concluded that river agency typically sets the schedule with given trip dates and
types for prospect tourists to choose from, while the specific route of a given trip is
up to the tourists in order to provide them with flexibility and freedom. (Note that
only the campsites where the ship stops matters in the problem, and we will use the
word route to denote the campsites throughout the paper.) Also tourists usually take
sleep at the campsites and go on along the river in the day, so they only travel in the
downstream direction and spend only one night at a certain campsite.
We regard the carrying capacity of the river as the maximum total number of trips
available each year, hence turning the task of the river managers into looking for the
best schedule itself. Given the actual practice mentioned in the previous paragraph,
we want to develop mainly three types of schedules, in terms of the flexibility of the
trips. In the part 1, we will design a schedule with fixed trip dates and types and also
routes. In the part 2, we design a schedule with fixed trip dates and types but
unrestrained routes. In the part 3, we design a schedule with fixed trip dates but
unrestrained types and routes. As one can imagine, the maximum number of trips
should decline in the order of three schedules because of less control on travelers’
trips, and the final choice of the three schedules should be up to the managers, with
consideration of commercial and management issues.
2 Definitions
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