stable marriage/residency problem with multiple matches

Consider the stable marriage problem, where both sides want to match with multiple individuals from the other side (perhaps a fixed number, or perhaps within some range). Something like, if doctors could choose to go to more than one medical school at the same time.

Is there a variation on the deferred acceptance algorithm to handle this generalization? Can I just have each "doctor" propose to n hospitals at each step, where n is the number of hospitals he is trying to attend at once? Also, what if hospitals do not have preferences?

• I find it unclear exactly what the problem is and what the constraints are. Do you know in advance how many hospitals each doctor needs to be matched to, and how many doctors each hospital needs to be matched to?
– D.W.
Jun 7, 2018 at 21:32
• Yeah, sorry, you do know that in advance! I did some more digging, and I think the normal way to describe what I was thinking about is close the many-to-many stable matching problem (with substitutability). The solution is the expected extension of the delayed acceptance alg. The only thing is, I haven't seen anything about what to do if one side doesn't have preferences, or might have ties in preferences. Jun 8, 2018 at 2:12