How to distribute professionals in a schedule in Google Sheets

Question

I'm working for a client and they want me to distribute their professionals, which have different availability each in a schedule (always 1 hour duration) of specific times with 3 categories of professional. Sometimes this professionals offer 1hour in a specific day of the week, others offer 10 different options of hours&weekday

They want also that the amount of subscriptions and the amount of participants to their work and a couple of other internal criteria be used to define a ranking to whom to give first a time in the schedule.

At the beginning it was easy because there were not enough professionals and we were able to distribute them all. But now and every month there are more professionals and there are some times from schedule that can't be filled in even though we have enough people to fill it out.

I first built a table to rank them. Then using VSTACK I brought it in order with their name, amount of available hours and calculated a value considering if the time they choose was one almost no one offered himself/herself to work on (like sunday morning) or if it was a time that almost everyone was willing to work. And also a column with their punctuation from table ranking

Based on those criteria I sorted them to start distributing the schedule.

To define which times would be filled first, I used the criteria of the ones with less people available.

And even using all this criteria I still can't distribute them all. How can I force Google Sheets to really fill all the available times and give priority to the professionals that work best (or a different tool, I know a little of R, know Apps Script, VBA, Excel... and am willing to learn Python or anything that might resolve this for us that is accesible for the company's department)

Thank you for reading and trying to understand my problem, any idea of solution is welcome to help me think a way out.