Hi, I need some help in designing a work rotation equitably. That is, ensuring everybody receives an equal number of shifts of each type (E, 1230, and 1100) based on their FTE (full time equivalant).

8 people at 1.0 FTE
3 people at 0.8 FTE
2 people at 0.65 FTE
3 people at 0.5 FTE

The shifts to be divided equitably:
160 - E (evening) shifts
80 - 1230 shifts
80 - 1100 shifts
(the 1230 and 1100 simply refer to the shift start times)

I am assuming their is an equation to assist in this task. I need to make sure that the lower FTEs (.8, .65, and .5) have an equitable portion of these shifts compared to the 1.0 FTEs. How do I solve this challenge? Of course I need the answer to this problem but greatly interested in the process as I predict being faced with this challenge again in the future. Thank you, Lee.