I am solving a scheduling problem-to find shifts and task schedules- using column generation. In essence, it is a set covering problem with additional constraints. The problem seems to be that the duals used to find task schedule columns do not provide much information regarding shifts schedules, e.g., tasks are scheduled in periods where shifts coverage is not allowed.
Is it possible to heuristically adjust the duals in such a way that information such as shifts coverage is incorporated in the reduced cost and thus used when finding new task schedule columns? How can we find "better" duals?