Scheduling - Maximum flow?

[hello99]

Hello,

Lets say we have a number of emplyees N. Each of these employees must specify which 15 hours of the week they are available to work their shifts. Now we want to give each employee 5 hours of work in a week. So we want to do some kind of matching to maximize the number of shifts assigned.

Also, what if there are some constraints like: if there are more than one possible answer, then we want to prioritize the older employee. i.e. If two employees have the same number of shifts assigned to them, and we still have one shift that can be given to one of two employees, then we would like to give that shift to the older one.
And probably, we will not like to assign to an employee many shifts in a day which have many breaks in between. So we might want to give emplyees shifts that are continuous.

I think this is related to maximum flow. I'm planning to use this in a database system, where I can collect time slots from the employees and run the algorithm to find the solution, and I do not want to re-invent the wheel, so I wanted ask here to check if you can provide me with any code (preferably C++) that I can use instead of doing everything from scratch. Also, are there any existing applications which does this, can you give their links?

If you know anything about this please reply
Thanks alot