COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics

## WSU Teams Compete in the Montana Mathematical Modeling Challenge

Three WSU interdisciplinary student teams, Primary Factorial, Irrational Proposition, and Derivators, recently competed in a 24-hour-long Montana Mathematical Modeling Challenge (MMMC) on the weekend of October 20-21, 2018 at Carroll College in Helena, Montana. The students traveled with mathematics and statistics faculty members, Dr. Lynn Schreyer and David Hampson, on a beautiful fall weekend. For some of the students it was their first time visiting Big Sky Country, and only two of these eight adventurous students had know each other prior to the trip.

On Saturday morning students were given the option to choose from one of two open-ended problems, which they had to solve within 24 hours. They were then required to turn in a two-page executive summary of their solution by 9:00am the following morning. Oral presentations to the entire group began at noon on Sunday.

The first problem the students could choose from was to determine whether a city should put in a bid to host the Summer Olympics Games. Students were to develop a mathematical model by identifying key variables and parameters that any city or metropolitan area could use. They then had to use their mathematical model to identify 5 eligible cities.

The second problem involved bike-sharing services in Seattle, Washington. The goal was to determine the location of 3 distribution centers where excess bikes could be returned at the end of the day before being redistributed the following morning.

##### Primary Factorial

(Richelle Thompson, Dexuan Luo, and Gillian Gormley)

The Primary Factorial team consisted of Richelle Thompson (applied mathematics), Dexuan Luo (business), and Gillian Gormley (mathematics). Their team chose the bike distribution problem. They began by considering two different tracks – one using statistics and the other using a mathematical (non-statistical) approach. As Dexuan said, "After we overcame the communication and cognition barriers, this diversity became the most valuable asset to our team." They had fun when they noted that the provided data did not include Husky Stadium (Go Cougs!). Toward the end of the 24 hours, Gillian suggested: “Instead of changing our model to be better, let’s just come up with reasons why other models are inferior.” Their strategies worked and their team was evaluated to be second overall for their approach and written summary.

##### Irrational Proposition

(Nik Steckley, Tom McCutcheon, Patrick Morrell)

Irrational Proposition consisted of team members Nik Steckley (theoretical mathematics), Tom McCutcheon (applied mathematics), and Patrick Morrell (computer science) who also chose the bike distribution problem, yet to solve it their team decided to employ a Markov Chain strategy. When asked why they applied this modeling approach Nik said, “I had heard of it only once before when a particularly passionate MATH 220 linear algebra instructor I had a few years ago exposed me to it as bonus material at the end of lecture one day; he used it to solve a similar problem for determining where taxi cabs would be distributed at the end of the day.” They first had to familiarize themselves with Markov Chains and their initial attempt was not exactly what they expected. Patrick contemplated, “Hmmm… why is one of the locations for the distribution center in the Pacific Ocean?” Tom then said, “If we’ve built the transition matrix correctly, all the columns should add up to one .. why is that one 3?” Eventually they worked everything out with the proper constraints, and their results passed the “common sense” test. Their team ended up being a finalist in the oral presentation competition, implying that other teams working on the same problem respected their work and explanation.

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##### Derivators

(Grace Harris, Elyce Cederholm)

Team Derivators Grace Harris (electrical engineering) and Elyce Cederholm (chemical engineering) took on the challenge of developing the Summer Olympics bidding model. They immediately recognized that financial profitability could not be a motivator since every city loses money, so they looked at other factors. While other teams considered hotel space, airport capacity and public transportation, the Derivators instead took into consideration the environmental impact, incorporating the recycling rate, using renewable energy as a percentage of total energy consumed, and the effect of land-loss due to new construction. They used a completely different approach than any other team working on the problem, and for this they received the most creative modeling award.

###### Students wait for the problem reveal (below)

(Back row: Nik Steckley, Tom McCutcheon, Patrick Morrell. Front row: David Hampson, Dexuan Luo, Richelle Thompson)

###### Primary Factorial (below)

(Richelle Thompson, Gillian Gormley)

###### Irrational Proposition (below)

(Nik Steckley, Tom McCutcheon, Patrick Morrell)

###### Derivators (below)

(Grace Harris, Elyce Cederholm)