Great to see this post here -- really enjoyed writing it! I think it's really cool how an algorithm from an operational research context can play a critical role in a high-availability large-scale cloud service.
Neat article. I do wish it mentioned that there are polynomial time algorithms to solve linear programming problems. According to the Google ortools docs it has the option to use those as well (but not with the GLOP solver). Might be good for when simplex is struggling (<a href="https://developers.google.com/optimization/lp/lp_advanced" rel="nofollow">https://developers.google.com/optimization/lp/lp_advanced</a>)
> X = [x1, ..., Xn]: instances of each type to launch<p>Is this a continuous variable? Seems discrete to me. I am surprised it is solved by simplex.