But deciding how many nurses to have at what time, based on the probability of how many and what kind of patients and the likelihood of a good medical outcome is a different problem.
Scheduling problem (the general one) maps easily to the vehicle routing problem. Vehicles are routed and service customers. On-demand requirements and scheduling are probably easier to conceptualize in that framework (think Uber but with ride-sharing bus sized cars, or team picking up and delivering food from restaurants to locations, or repairmen doing stuff at people homes).
All needs combinatorial search and machine learning is only one little piece of the puzzle.
ML includes optimization/search, dimensionality reduction (aka unsupervised learning), prediction (aka supervised learning), and reinforcement learning. And I'm probably forgetting a category.
IMO, ML is nowhere close to useful in these problems when most of the clients just use pen and paper. It should be fairly easy to beat that with some simple search heuristics.