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# California Students Clinch Top Prize for Mathematical Approach to Food Insecurity

#### 2018 MathWorks Math Modeling Challenge Addresses Food Waste

Many Americans take for granted consistent availability of a nutritious food supply. Yet according to the United States Department of Agriculture (USDA), nearly 13 percent of U.S. households—equivalent to over 41 million Americans—experienced food insecurity in 2016. Food insecurity is defined as a state of living in which one lacks reliable access to a balanced source of food that permits a healthy, active lifestyle.

Furthermore, the Food and Agriculture Organization of the United Nations (FAO) estimates that approximately one third of all food produced in the world is wasted each year due to disfigurement, overstocking, impulse buying, excessive portioning, and unreasonable quality standards. This uneaten food comprises the bulk of landfill and incinerator content in the U.S., thus squandering the valuable labor, land, and water resources necessary for production. Can wasted food be used to feed food-insecure populations? If so, how can agencies effectively and economically repurpose the waste?

These are the kinds of complicated, multifaceted questions explored in this year’s MathWorks Math Modeling (M3) Challenge, which tackled food insecurity and the reduction of food waste in America. Sponsored by MathWorks and organized by SIAM, the contest invites participating teams of U.S. high school juniors and seniors to address a complex, real-world problem—akin to those faced by professional mathematicians and computational scientists—in 14 hours using mathematical modeling. After two intense rounds of judging—one via an online platform, followed by a second at SIAM offices—collectively involving roughly 130 SIAM member judges, the top six teams were invited to travel to New York to present their solution papers to a final panel of judges and compete for scholarship money. The concluding round was hosted by Jane Street, a quantitative trading firm.

This year’s Challenge problem asked teams to create a mathematical model to determine whether the state of Texas could feed its food-insecure population using food waste from the state. Participants then had to develop a second model to calculate the amount of food waste produced yearly by different types of households with varying income levels. Finally, they were to suggest a strategy for repurposing the maximum amount of food for the least cost.

“These are the very types of questions that we look at in our research,” guest judge and USDA agricultural economist Pat Canning said. “We look not at short-term, but medium- and long-term policy-relevant issues. Food security is obviously one of our most important issues, and many have identified food waste as a promising area of research for achieving technological advancements.”

In his opening remarks, Canning emphasized mathematics’ relevance to the social sciences—specifically agricultural, natural resource, ecological, and environmental economics—by describing his recent projects. One task involved the use of an environmental input-output multiplier model to gauge whether healthier diets generate lower greenhouse gas emissions and use less fossil fuels and fresh water. For another, he utilized computable general equilibrium models to examine the Supplemental Nutritional Assistance Program’s effect on farm output and farm employment.

This year’s first-place team, from Los Altos High School in Los Altos, Calif., began by consulting government databases and FAO resources to become familiar with food waste and food insecurity. Using this data, the students identified a production waste vector, calculated the percentage of different types of food waste in Texas, and converted the resulting numbers to kilocalories per dollar. They summed up these values and divided them by one’s average daily caloric needs to determine the number of people that the state’s food waste could nourish. Based on a 2,000-calorie diet, the team concluded that Texas’ waste could feed 1.95 million of the 4.32 million food-insecure residents. “That’s on the assumption that we’re feeding food-insecure individuals their entire diet,” team member Michael Vronsky said. “If we wanted to actually distribute whatever food we had across the population, we could have covered about 40 to 50 percent of their diet.”

For the second question, the California team calculated the average number of calories required per day for people of different ages, genders, and activity levels; this established a baseline for four different household types with a range of incomes. The students then used a nonlinear regression on the consumer behavior data set to predict the proportion of income each household spent on different food types, such as vegetables or grains. From this information, they estimated the amount of food (in pounds) wasted by a single parent with a toddler, a family of four, an elderly couple, and a single 23-year old: 256.4, 839.9, 366.8, and 217.2 pounds respectively.

Identifying the delivery of repurposed food waste to the food-insecure as a primary setback, the Los Altos students experimented with three delivery strategies for their county: one central distribution center, multiple distribution points, and a centralized distribution facility with mobile freezer trucks. Employing computer simulations to measure the strategies’ effects on both recipients and the state, the team examined the availability of distribution methods, the distance and travel necessary to obtain repurposed food, and the associated economic costs and benefits.

“We used results from the simulation, along with some of the cost data associated with created distribution centers, like the cost of actually building one and wages for truck drivers who work in the centers,” team member Joanne Yuan said. “With this information, we calculated a net gain function to see which strategy would be most effective.” Assuming that food-insecure individuals would only travel to distribution centers if the value of the food was greater than the cost of transportation and the potential loss of work due to travel, the team concluded that a multi-hub model—of which 90 percent of food-insecure people would take advantage—would be most effective in the long-term.

In addition to Vronsky and Yuan, the Los Altos champion team—which will split $20,000 in scholarship funds—included seniors Ryan Huang, Daniel Wang, and Justin Yu. The group also nabbed the top M3 Technical Computing Scholarship Award, new in 2018 and presented for “outstanding use of programming to analyze, design, and conceive a solution for the problem,” which yielded an additional$3,000 in prize money. Members agreed that seeing a concrete result of their hard work was gratifying, and praised the competition’s practical nature.

“The problem is good prep for a real-world experience,” Huang observed. “What we did in the Challenge is similar to what a lot of consulting firms do—analyzing problems with a team, writing a paper that explains our ideas, doing analysis, and creating assumptions—which is also really important for modeling in the real world. It’s definitely good practice for the future.”

Los Altos coach Carol Evans echoed her students’ approval, acknowledging that high school curricula typically do not expose students to much mathematical modeling. “With the exception of statistics, other high school math classes tend to be more formulaic and very procedural,” she said. “So this is a great opportunity for the kids to put it all together. I see skills from their algebra II classes, their stats classes, and a variety of other classes; that doesn’t happen a lot in high school math curricula.”

Champion team members expressed interest in pursuing careers in science, technology, engineering, and mathematics—from bioengineering to computer science—and their success inspired a hearty dialogue about potential employment opportunities and future areas of study as they move on to college in the fall. This is exactly what the M3 Challenge hopes to achieve. “Students have tremendous tensions pulling on them, and we want to keep them looking at math as something they can do with their lives,” MathWorks cofounder and Challenge judge Cleve Moler said. “Throughout their elementary and junior high school education, they haven’t seen much that is exciting about math. This is one of the first examples they encounter of how math can be exciting and important.”

 Lina Sorg is the associate editor of SIAM News.
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