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You need piecewise linear cost function and auxiliary variables. An experienced practitioner should be able to help you with either mixed integer linear program

You need piecewise linear cost function and auxiliary variables. An experienced practitioner should be able to help you with either mixed integer linear programming or constraint programming

rosstex 2y ago
This feels like a basic service Timefold would offer...
LDWNS 2y ago
No need when using the timefold solver, the constraint streams allow for a more "human readable" approach. e.g. Penalise when the minimum is not reached, Penalise when the maximum is exceeded (2 constraints).