✍️ Max Kapur

📜 Master’s student

🏛️ Management Science/Optimization Lab, Seoul National University

Try to decide which colleges to apply to, given

- the
**utility**associated with each school, - the
**probability of being admitted,** - each school’s
**application fee,**and - a
**total budget**to spend on applications.

*Maximizing the expected maximum* of a portfolio of random variables: a challenging combinatorial optimization problem.

Special case: All application fees equal. `applicationorder_list()`

and `applicationorder_heap()`

are **quadratic-time algorithms**.

General case:

**Exact solution**from`optimalportfolio_dynamicprogram()`

or`optimalportfolio_branchbound()`

.**ε-approximate solution**from`optimalportfolio_fptas()`

.**Heuristic solution**from`optimalportfolio_simulatedannealing()`

.

**Multiple dispatch, parametric types** ⇒ easy to accept different kinds of user input and preserve type stability

**Easy to parallelize** validation study with `@threads`

Simplicity of **creating and sharing packages**

OptimalApplication.jl could be a lot **more generic**, e.g. accept DataFrames.jl series as input.

Integrate with Bonobo.jl to handle **more sophisticated constraint structures** that arise in real-world admissions markets.

Graphical interface/web app.

OptimalApplication.jl:

`]install OptimalApplication`

- Source code and documentation on GitHub.

Theory: github.com/maxkapur/CollegeApplication hosts an arXiv paper and various conference slides (including these).

Me: Julia Discourse, LinkedIn, GitHub, personal blog.