i work in a company that gives service to peoples (hundred a day),
we deal with several types of clients (the types are known ahead for each client)
each client type need certain services from the company, and for the same service people from different types need different amount of time.

the clients come by pre-ordered meetings which i summon, they may not come, but the chance of not coming is already calculated.

i have constraints of:
1) list of clients (and types) need to be dealt with, until a certain date.
2) work hours of my workers which supply the service.

data i have in advance:
1) time for each employ in each service (he can give) for each client type

i need to find a list of how much people from each type i need to summon for each hour, in a way that my employs will have constant work,
almost every client i will call will end all (if possible) of the activities needed at the day summoned so i will dont need to call him again

which mathematic model should i use and how?
(i dont know how to define the target function i need)

10x for the help