Many cities allow families to choose elementary schools to address growing inequities in school instruction and performance. School choice lets families give a rank ordering of their preferred schools, and a lottery ultimately assigns students to schools. The result is that many students have to travel a long way to school, crazy bus schedules, and students on the same block who do not know each other because they go to different schools.
Peng Shi at MIT (with advisor Itai Ashlagi) won the 2013 Doing Good with Good OR Award held by INFORMS with his project entitled “Guiding school choice reform through novel applications of operations research” that addressed and improved Boston’s school choice model. I am pleased to find that his paper based on this project is in press at Interfaces (see below).
The schools in Boston were divided into three zones, and every family could choose among the schools in their zone. Each zone was huge, so on any given block, students might be attending a dozen different schools. See a graphic in a Boston Globe report to see more about the problem.
Peng balanced equity with social problems introduced with the choice model by proposing a limited choice model. His plan was to let every family to choose among just a few schools: the best and the closest. Families could choose from the 2 closest in the top 25% of schools, the 4 closest in the top 50% of schools, and the 6 closest top 75% schools, the 3 closest “capacity schools,” and any school within a mile. There was generally a lot of overlap between these sets, so families had about 8 choices in total (a lot less than the original school choice model!). This gave all families good choices while managing some of the unintended consequences of a school choice system (busing and transportation, distant schools, neighbors who didn’t know each other).
The model itself was not obvious: there is no “textbook” way to model choice. Peng visited with the school board and iteratively adapted and changed his model to address concerns within the community. This resulted in the model becoming simpler and more transparent to parents (most parents don’t know about linear programming!). The new model pairs above average schools with below average schools in a capacity-weighted way to make school pairs have comparable average qualities. This lets families choose from school partners, the closest four schools, and schools within a mile.
The school board voted to adopt his plan. Peng worked with the school district to come up with important outcomes to evaluate. The model itself uses linear programming to “ration” school seats probabilistically among students by minimizing the expected distance subject to constraints. To parameterize the model, he used a multinomial logit model to fit the data (with validation). He also ran a simulation with Gale-Shapley’s deferred acceptance algorithm as a proof of concept to ensure that the model would work.
I’ve been on the INFORMS Doing Good with Good OR Award committee for the past three years. This award honors and celebrates student research with societal impact. I love this committee – I get to learn about how students are making the world a better place through optimization. And these projects really do make a difference: all applications must submit a letter from the sponsor attesting to improvements. Submissions are due near the end of the semester (hint hint!)