Ask HN: Constraint Solving Libraries for Automated Scheduling?

I've been searching for an existing scheduling solution where the primary goal isn't filling set shift times, but instead supplying a certain amount of coverage at each hour of the day based upon a set of constraints (listed here: http://www.nathanhammond.com/a-scheduling-problem).

There are two existing categories of businesses that come to mind that might have this type of use pattern:

    * Medical facilities
    * Call centers

I've reached out (via phone!) to multiple companies that provide services to these business categories but I've been told by salespeople that they either don't have this sort of functionality, that it is so specifically tailored to the target market as to be useless to me, that I shouldn't be pursuing this (!), or they assume that because I'm doing this for a non-profit I'm not willing to pay for it (my money is just as green!).

At this point (unless you're aware of somebody that will sell their product to me) I was wondering what tools I should use to build this.

My first thought was to use something like Prolog, but because I'm not expecting there to be a "perfect" solution, I don't know how I would make that work.

After a bit of research I found Drools Planner which appears to be the 800lb gorilla, but before heading down that path I was wondering if any of you were aware of other lighter-weight tools that would make this easier to build in my spare time?

Thanks!