Sounds like a typical OptaPlanner problem.

Domain model:
- CareTaker
- OldPerson
- Day
- Visit(OldPerson, Day)
- @PlanningEntity VisitAssignment (Visit, @PlanningVariable CareTaker)

Using the OptaPlanner employee rostering example:
- CareTaker == Employee
- OldPerson == ShiftType
- Day == ShiftDate
- Visit(OldPerson, Day) == Shift (ShiftType, ShiftDate)
- @PlanningEntity VisitAssignment (Visit, @PlanningVariable CareTaker) ==
ShiftAssignment (Shift, @PlanningVariable Employee)



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