I think the bailiwick you're looking for is program management, rather
than project management.  Here's a scary product page from HP that
seems to address this:

https://h10078.www1.hp.com/cda/hpms/display/main/hpms_content.jsp?zn=bto&cp=1-11-16-18^1313_4000_100__

I'm willing to bet that HP PPM is heinously expensive, and intended to
be run by a cadre of certified PMPs.

Some program management can be done by rolling up projects in the
program portfolio as tasks in a higher-level project plan, and then
using a project management tool to model the program.  MS Project is
actually pretty handy for this; it won't do automatic resource
assignment, and absolutely won't go near "I have 10 more-or-less
interchangable resources of this type, please assign them to tasks,"
but if you assign resources to tasks, it can show you when resources
(actual people, rather than categories of people) are horrifically
overloaded, and then you can tweak the calendar or staffing to reduce
the load and view the result.  I've often felt that task assignment
should be part of what MS Project (or any of the project management
tools) does, but I guess there's a complexity to the problem I've not
grasped, so nobody has implemented it.

Program management tools are probably not in the free-to-cheap
category, but examining their features may give you ideas about how to
approach the problem without laying out a fortune for a tool.

    Pete.
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