Depends on the problem Cbc [1] is modern, free and is competitive for most non-complex problems like timetabling (say less than 100k variables). (Cbc is much b

Depends on the problem Cbc [1] is modern, free and is competitive for most non-complex problems like timetabling (say less than 100k variables). (Cbc is much better than GNU Linear Programming Kit -- GLPK -- which uses outdated algorithms and is not competitive). Cbc can also be called from Excel via OpenSolver. Scip [2] is the most performant "non-commercial" solver, but is only free for non-commercial uses. Commercial uses require licensing. As for writing MIPs, this FICO MIP formulation guide [3] is extremely well written. Modeling MIPs is something of an art, and this doc captures most of the common formulations. [1] https://github.com/coin-or/Cbc https://github.com/coin-or/Cbc [2] https://scip.zib.de/ https://scip.zib.de/ [3] https://www.fico.com/en/resource-download-file/3217 https://www.fico.com/en/resource-download-file/3217