Ok, based on what I understand of the problem now, I'd consider something like this:
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This would be the design per cell in your planning grid. The idea is to show the employees working that day directly in the cell, and you can add new employees to the list from a little popup that appears if you click the + icon. Depending on your needs (and like Igor-G already suggested), you could also allow other ways to add persons, for instance by somehow activating an employee from your side list, and then clicking every cell he needs to be added to. That would make it much faster to add a single employee to multiple days. I'd also consider the option to copy a previous schedule into a new week, so you don't have to go from scratch every time. Normally, schedules tend to be fairly regular with some exceptions here and there.