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Q&A with Los Altos High’s national math champions

The Town Crier conducted online interviews with three of the five Los Altos students who won the top prize of $20,000 in college scholarships from this spring’s MathWorks Math Modeling (M3) Challenge.

Q: Your task was to develop model-based strategies to quantify, reduce and repurpose the most food for the least cost. What exactly did you come up with for that?

Ryan Huang: To quantify food waste, we created two models: one that examined if the food wasted by Texas could be used to feed its food-insecure population, and another to determine the food wasted by different households. In the first model, we used data on Texas’ food spending and percentage food waste by food type to find that Texas does not produce enough recoverable food waste to fully feed its food-insecure population. In the second model, we used consumer food spending data and USDA nutritional guidelines to determine the food waste for a given household (e.g., a single 23-year-old or a family of four).

To repurpose food waste, we modeled a food distribution strategy for Santa Clara County. Our model consisted of distribution centers where repurposable food waste would be dropped off by supermarkets, food manufacturers or other groups. The food would then be given to the food-insecure, either through a fixed (people must drive to the center to pick up food) or mobile (trucks deliver the food) strategy. We used a computer simulation to analyze the efficacy of this model. We also varied the parameters of this model to determine the best strategy. Our results point to four fixed distribution centers as the best out of the three we analyzed.

Michael Vronsky: The problem statement had three parts.

The first part involved answering the question of whether Texas could use its food waste to feed its food-insecure population. We developed a model based on many conversion factors and found that while we could not fulfill a full 2,000-calorie diet for the entire food-insecure population, we could theoretically distribute about a maximum of 905 calories per food-insecure individual.

The second part of the problem asked us to model consumption waste for various households. A unique aspect of our model is that we modeled how food preferences change with income, and used that information along with waste percentages and caloric need to determine the food waste generated by each household.

The third part of the problem asked us to come up with an analysis of our own food distribution strategies. We used a computer simulation to model consumer benefit and government costs of various plans, including building one central food bank, building multiple stationary food banks and using trucks to distribute food from a central bank. Ultimately we found that using four fixed distribution centers was the most effective after 4.8 years. The primary strength of our model in that section was that it could theoretically be extended to many other strategies quite easily, allowing us to theoretically examine the efficacy of many more strategies.

Joanne Yuan: For the first part, we were given the task to see if the food-insecure population of Texas could be fed with the food waste produced. In this problem, using the data provided and excluding consumption and production waste, we found that only about 1.95 million individuals out of 4.32 million food-insecure individuals could be adequately fed.

For the second part of the problem, we were asked to find the amount of food waste for specific households given information such as number of people in the household, ages, income, etc. For the last part of the problem, we looked at how distributing food to food-insecure individuals, specifically in Santa Clara County, would work. We considered three scenarios with this: one fixed distribution center, four fixed distribution centers and four mobile distribution centers. We found that, in the short term, four mobile distribution centers is most effective; after about 4.8 years, four fixed distribution centers becomes more effective.

Q: Were the other teams given the same task or something slightly different?

A (from all): All of the 913 teams were given the same task.

Q: What made your team stand out in the competition?

Huang: By taking into account how income affects the types of food people buy (and thus consume), our model acknowledged that different people have different food preferences. For example, some people eat more fruits and less meat than others. This made our model more precise, as food waste depends on food type.

For the fixed distribution centers in the third problem, the computer simulation modeled each food-insecure consumer as a rational agent. A consumer would only travel to a distribution center if the benefits of receiving the food outweighed the costs of gasoline and lost wages (due to time lost to driving). This model captured the crux of the problem of food distribution centers, which is actually getting the food to people. Also, by framing it as an economic problem, we were able to easily compare different strategies.

Vronsky: In my opinion, there were two things which made our paper stand out the most. The first was our modeling of different food consumption by income. After winning, we received feedback from one of the judges that this aspect of our paper was one of the things that the judge was personally looking for in papers, and that it helped us stand out against other teams.

I also think our use of a computer simulation to model food distribution was unique. We used that simulation to estimate what percentage of food-insecure individuals in the county would want to go out of their way to get food from a distribution center, and what benefit they could expect from that trip, factoring in costs such as gasoline and lost wages (opportunity costs). This simulation was what earned us the technical computing award, but I believe it also played a large role in winning the main competition.

Yuan: I think something that made us stand out was our solution to the third problem. Some of the teams chose to consider multiple different solutions, but we decided to focus on one solution, and I think that we had more time and could do a more in-depth analysis.

Q: Can your winning strategies be easily applied to daily life?

Huang: Not exactly. Our strategy in part three operates at the county level and not at the individual level. However, people can still help by donating to such centers.

Better yet, people should make more conscientious choices. In our research, we found that consumption waste (e.g., food wasted after it has been bought from the store or served at a restaurant) usually cannot be donated or repurposed. Luckily, it is easy for people to reduce consumption waste by not buying or ordering too much food at the supermarket or restaurant.

But again, reducing food waste at the individual level was not the focus of our research or solution. There are good guides out there for how to do so, and I would encourage others to look at those.

Vronsky: Our solutions to the first and third parts of the problem are primarily aimed at larger-scale policy change on the part of the state or county. For those models, we would encourage a more in-depth analysis (due to the short amount of time we had to complete them), but we think that our solutions provide a starting point for methodologies that could be used to model policy. Observations from our second model could provide some insight on everyday life, but aims more at modeling the outcomes of food waste, and less at creating solutions for mitigating it.

Yuan: I think the skills that we’ve learned in this competition will prove to be valuable in the future.

Q: How did teamwork help you win?

Huang: Teamwork was necessary for us to complete the problem in the 14 hours we had. The sheer amount of writing and research could not have been done by one person. Also, by working together, we did not get stuck in dead-ends. Instead, we could bounce ideas off each other and explore multiple pathways at once. Teamwork also helped us stay focused and motivated, especially into the late hours when fatigue set in.

Vronsky: Teamwork was incredibly important to our process. During such a narrow and intensive 14-hour window, it is very easy to stop working well together and get tired and frustrated. When we competed last year, many of us did not know each other (personally, I was even struggling remembering names an hour into the challenge). Since then, we have become much closer, competing in other math modeling competitions and preparing for this one. Our work this year was very cohesive, and we were able to stay strong throughout the entire work window.

Yuan: Each of us had our own strengths, so we could focus on different parts of the problem and work together to write our solution paper.

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