Obviously, if processing the whole set is too much,
you need to break the problem up.
Perhaps you could create service areas for each hospital individually,
using a maximum acceptable travel time.
union the polygons of hospital areas,
The single hospital parts represent eash hospital's unique core area
the overlaps tell you which hospitals could potentially service that area.
for each cluster of overlap polys, run allocation for just the hospitals that
are potential servicers
Ignore any allocation outside the selected overlap polygon (or cluster of polygons)
because outside the selected cluster there may be other hospitals,
not included in this round, affecting the allocation.
working through the overlap polys will resolve the potential conflicts
and restrict your analysis runs to just the hospitals participating in the conflict area.
