What are some algorithms that can assist with reservation time scheduling?

What are some algorithms that can assist with reservation time scheduling?

Here's the gist of the problem: There are multiple service providers who
each have their own schedules of availability. There are multiple
customers who seek their services. Customers need to be able to book a
reservation time for the service but they should only be able to book
times in which some service provider is available (ie they don't really
care which particular provider they get so long as they get a provider).
Unfortunately, service providers may change schedules between when the
customer registers and when the service is provided, meaning that even
with the reservation safeguards in place there could still end up being
too many reservations for a given time.
I would like to know what work has already been done on this sort of
problem, and additionally:
Should providers actually be "assigned" to customers in a persistent way
even though providers are interchangeable?
Depending on the answer to the previous question, how might I determine
the provider's "next assignment" based on the current time, other
providers' schedules, and scheduled reservations?
I've thought a lot about this problem but I am stumped and left with
unsatisfying solutions. As someone with no CS background I would
appreciate some insight and/or a better way to think about the problem.