Students in Professor Gianluca Guadagni’s spring 2018 Stochastic Methods course are winners of an international applied math competition.
Fourth-year engineering undergraduates Taylor Arnold, Alex Baker, Alden Duquette, Nirali Jantrania and David Josephs, and third-year physics/math major Charlie Maier, participated in the ninth annual Mathematical Competitive Game held jointly by the French Federation of Mathematical Games and the Mathematical Modelling Company Corp.
There are first-, second- and third-place individual and team awards. Guadagni’s students placed first, earning 500 Euros for the team. Each year, the competition requires the students to solve a simulated real-life problem, such as conceiving a bus transportation network or an electricity distribution network. The 2017-2018 game, “Distribution of Goods,” tasked students with answering a number of questions related to producing and delivering two products through two manufacturing plants and distribution facilities that included four warehouses and 20 retail stores.
The students devised a delivery plan for a hypothetical new owner of the company for the year 2018. They assumed the new owner took over with zero inventory on Jan. 1 and they could use only what production, sales and distribution data they could find from previous years. Missing information was an integral part of the exercise.
Guadagni said the goal of the stochastic methods class is to familiarize students with modelling methods that are not exact, but that leave room for randomness, uncertainty and imprecision.
“We went over several topics that are standard in research, to show how effective they can be even with their uncertainty,” Guadagni said. “For instance, we saw how to mathematically describe financial options; this does not mean we can predict what their prices will be tomorrow, but we can certainly compute a range of probabilities for those values, based on some assumptions.”
He referred to assumptions in terms of figuring out what “corners to cut” when it came to solving the competition’s distribution problem. Even when the students were stuck, he reserved his own role to playing devil’s advocate, criticizing the efficacy of the models they tried, and “stressing the value and importance of aspects they had simplified or eliminated,” he said.
“I am proud to say that I never told them how to solve an issue. My goal was to let them understand the inescapable responsibility of making choices: If you want to solve a complex problem and you have to accept approximations, then to find a reasonable or satisfactory solution, you have to cut corners. The hard choice is to decide which are the corners to cut.”
Cutting corners makes your problem easier, Guadagni explained, but cut too many and the problem becomes irrelevant. “It is always a balance of what you give up in describing your system,” he said, “and the correspondence that the reduced model has with the system you want to describe.”
Arnold said the contest’s biggest challenge was being constrained to creating an immutable delivery schedule.
“We would research ideas the day before class and present them to the group and receive input. Half the team worked on optimizing routes for distribution while the other half attempted to find correlations between different parameters based on data sets provided by the competition,” Arnold said.
According to Maier ― whose algorithm they eventually submitted as their solution ― that kind of teamwork ultimately won the day. The problem statement was vague and their interpretation of it evolved as they tried to find the answer, Maier said.
“In addition, there was no clear floor cost, and it was hard to get an idea of how efficient our ideas were. We had to use metrics other than just cost to get an idea of how we were doing, and competed against each other with different algorithms to get a better idea of the floor to possible solutions.”