[wenc]

I used the Williams book in grad school and it provided context and motivation for MIP (mixed-integer) modeling, but for real-world MIP modeling, this guide from FICO is actually much better for practitioners.

This is the cheat sheet for MIP that I wished I had when I started out. It lays out all of the most useful MIP formulations in a simple and compact way.

https://www.msi-jp.com/xpress/learning/square/10-mipformref....

[7thaccount]

Thanks for the tip!

[wenc]

Just throwing another tip out there: if you're finding yourself having to model anything mildly nonlinear, but find yourself shackled by the linearity constraints of a Mixed Integer Program (MIP), you can use a statistical/ML technique called MARS [1] to regress a piecewise-linear model from your nonlinear data to approximate said nonlinear function. MARS models are essentially models with constant or max functions as basis functions, e.g.

y = a₀ + a₁ max(0, x − b₁) + a₂ max(0, x − b₂) + ...

max(0,x) functions are very easy to model in MIPs.

[1] https://en.wikipedia.org/wiki/Multivariate_adaptive_regressi...

[7thaccount]

I mostly just do LP & MIP (MILP), but will write this down in case I find a nonlinear need. Thank you!