[cweld510]

You're right -- we do relax the integrality constraint, gaining performance at the expense of some precision, and we're generally able to paper over the difference at scheduling time. We've investigated integer linear programming for some use cases, but for solves to run quickly, we have to constrain the inputs significantly.

[stncls]

If this is business critical for you, you may want to switch to a faster solver. Glop is very nice, but it would be reasonable to expect a commercial solver (Gurobi, XPress, COpt) to be 60x faster [1]. By the same measure, the best open source solvers (CLP, HiGHS) are 2-3x faster than Glop.

Actually, the commercial solvers are so fast that I would not be surprised if they solved the IP problem as fast as Glop solves the LP. (Yes, the theory says it is impossible, but in practice it happens.) The cost of a commercial solver is 10k to 50k per license.

[1] ... this 60x number has very high variance depending on the type of problem, but it is not taken out of nowhere, it comes from the Mittelmann LP benchmarks https://plato.asu.edu/ftp/lpopt.html There are also benchmarks for other types of problems, including IP, see the whole list here: https://plato.asu.edu/bench.html

[petters]

If you are able to paper over the fractional numbers and get a usable solution, an integer solver should also be able to find a feasible solution easily. Perhaps not optimal, but better than just solving the LP and rounding

[hustwindmaple1]

You are basically doing a heurstic. Your solutions are not guaranteed to be optimal. Integer programming is the way to do.

[ayhanfuat]

Thanks for the clarification. I guess it wouldn’t matter much if the numbers are large. Initially I thought they were mostly ones and zeros.