The school location problem
I’ve spent a few days thinking about a facility location problem that we might call the school location problem. The goal is to place schools to serve families, such that the furthest distance between any family and their nearest school is minimized. This problem is almost a -means or ellipsoid fitting problem, but its unusual “minimin” form makes it computationally challenging.
In the video below, and associated Jupyter notebook (GitHub, HTML viewer), I discuss the formulation of this problem, show to express it as a mixed-integer second-order convex program, and then solve a small instance using the Julia/JuMP/Juniper/SCS stack.
Here’s the video link.
Administrative vs. allocative efficiency
This fall marks my final semester of coursework, and penultimate semester overall, of the master’s course in industrial engineering here at Seoul National University. I’m taking courses in combinatorial optimization and advanced microeconomics, as well as continuing my study of college admissions markets as a research assistant in the Management Science/Optimization Lab.
Recently, I have been focusing on risk-averse behavior in college applications. In an ideal universe, college applications are completely standardized and there are no constraints on students’ ability to apply to many schools or on schools’ ability to assess a large number of applicants. In reality, many highly qualified students fail to apply to top schools because they doubt their ability to get in or receive a sufficient financial-aid package. For these students, the time and money required to submit an additional application to a so-called reach school takes away from time that could be spent refining an application to a target school. This opportunity cost is not trivial, because modern admissions offices strongly prefer students who tailor their personal statement to the characteristics and interests of the target school or program.
An economic view of the Korean college admissions market
Existing computational models of admissions markets tend to fall at one of two extremes: Either they envision a centralized admissions process in which the school board runs an algorithm that says which students go where, or a decentralized process in which colleges compete for the best students. But the Korean college admissions process cannot be adequately described in either of these terms.
Stable matching on Planet Money
Planet Money, an NPR show about economics, recently ran an episode entitled “The Marriage Pact” that deals precisely with my research topic. It’s a great episode that discusses both the basic ideas behind stable assignment as well as its applications in organ donation, job placement, and (my area of focus) school choice.
The episode begins with an interview with a Stanford econ student who designed a marriage market for his peers and managed to get 4111 of them to sign up for it. What a cool project! The student makes a few minor misstatements about the Gale–Shapley proposal algorithm that Planet Money leaves uncorrected. In this post, I want to offer a few corrections, not just because I can, but because in my opinion these marginal details are what make stable assignment an interesting and profitable research topic.
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They say that we perceive time by the accumulation of novel experiences, so that if you want to have a subjectively long life, you ought to do many spontaneous and hard-to-repeat things, but if you want to have a happy life, you ought to find one or two high pleasures that you can enjoy on a spiritual level and repeat the hell out of them, because they also say that on average, people derive more happiness from repeating a good experience than from trying something new.
You could write a linear program that targets your ideal mix of longevity and happiness and it would tell you exactly how many times to do this or that activity before moving onto something new. But what this calculus leaves out is the feelings of uncertainty that stain the transitions.
I am leaving Naju, after having grown accustomed to this routine, this commute, these faces, and I cannot say with any confidence that I have reached a joy plateau. Every week of teaching here has been better than the last: my skills have improved, my confidence has grown, and the teachers and students have become only more important to me. I could be happy like this for a long time. But.
But too much comfort has a way of smearing all the time together, so that the things that take place in a given day feel less like events and more like footnote references to proto-events hovering in the firmament of the distant past. I have already seen the river clog itself with duckweed; I have already looked down the street from all four of the intersection’s corners, trying to make the buildings line up with the trees. Upon inspection, a more sensitive man might look at these rhododendrons and see something more than last year’s blossoms in a different configuration, but I am a pattern-matcher by nature, too easily bored to remain a recluse. It is time for a new challenge.
As I wrap up my Fulbright grant, I am delighted to share that I have been accepted into the Government of Korea Scholarship program, through which I will be returning to Korea in the fall to pursue a fully funded master’s degree in industrial engineering at Seoul National University.
Thank you to all who have encouraged me.