Your problem is a scheduling problem. It has been well studied in operations research [1] / mathematical optimization [2].

Basically, you formulate your problem as a integer programming model [3] and use a solver [4] to solve it. You should check PuLP [5].

You can also ask your question at OR Exchange [6].

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

[2] https://en.wikipedia.org/wiki/Mathematical_optimization

[3] https://en.wikipedia.org/wiki/Integer_programming

[4] https://en.wikipedia.org/wiki/List_of_optimization_software

[5] https://pythonhosted.org/PuLP/

[6] https://www.or-exchange.org/