At first glance it looked easy, especially with helper column, see Shit1.
in D2 1, and two formulas (yellow cells) copied down as needed (countifs, sum, index, mod and counta in not complicated mix).
But then I noticed, the input table is arranged not by date, but by the case number, and it means non-uniform load for workers.
With excel 365 specific functions (unique, filter, sort) it can be done even as single column solutoion, but it's not short formula. Could be shorter if date and patient were in adjactent columns, without case numn=ber in between.
Anyway - for D2 and copy down:
I think that time to time the sheet shall be cleaned from outdated cases, to keep it working with reasonable speed. The old data can be kept in the archive,
For such cleaning, I'd temporarily sort the table on date and caseID ascending (see copy od sheet) and copy special as values and as formats only to archive top rows but ending with a row where assigned worker is the last worker from the workers list. Then remove these rows from main table and finally (see second copy of that seet sort back on case ID
Final comments: I expect using LET could make the formula a bit more readible, also a VBA solution could be a good idea, especially if based on worksheet_change event for columns A:C and E.
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