Mathematical Contest in Modeling, 2012
The first year I competed in COMAP's Mathematical Contest in Modeling (MCM) was 2012. MCM is a competition that challenges teams of students to clarify, analyze, and propose solutions to open-ended problems. The problems were released on February 9,2012 at 6:00pm. The papers were due on February 12, 2012 at 6:00pm. My teammates were Stephanie Martinez and Camilla Hutchison.
My team chose Problem B: Camping Along the Big Long River.
"Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish.. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long River’s rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one page summary sheet, prepare a one page memo to the managers of the river describing your key findings."
We approached this problem by using a greedy scheduling algorithm. We then used stochastic modeling to optimize the output. Our model takes inputs X and Y which represent current number of trips offered and the number of camp sites along the river.
1. Our model starts by creating a boat and randomly generating its type (Oar or Motor) and its travel length (6 to 18 days).
2. If there are already boats on the river, our model first moves those boats forward. Then the model places newly generated boats into the schedule.
3. Once our model has filled up one night with as many boats as possible, it moves on to the next night. It continues this until all of the nights are full.
4. The next step is to run a Monte Carlo simulation with 100 iterations.
5. Our program looks for the schedule with the most boat trips, and then outputs it as our final schedule.
The resulting schedule creates hundreds of boat trips. The types of trips consistently contain variation, allow for a secluded experience, and have a utilization of camp site efficiency of about 70%.
1. Our model starts by creating a boat and randomly generating its type (Oar or Motor) and its travel length (6 to 18 days).
2. If there are already boats on the river, our model first moves those boats forward. Then the model places newly generated boats into the schedule.
3. Once our model has filled up one night with as many boats as possible, it moves on to the next night. It continues this until all of the nights are full.
4. The next step is to run a Monte Carlo simulation with 100 iterations.
5. Our program looks for the schedule with the most boat trips, and then outputs it as our final schedule.
The resulting schedule creates hundreds of boat trips. The types of trips consistently contain variation, allow for a secluded experience, and have a utilization of camp site efficiency of about 70%.