Dynamic capacity allocation for long-term care: A Markov decision process approach with patient preferences

In this work, we study a capacity allocation problem in long-term care (LTC) facilities, where bed-blocking, the occupation of hospital beds by patients awaiting LTC placement, impairs emergency and intensive care unit throughput.
We model the problem as a discounted infinite-horizon Markov decision process (MDP) that simultaneously accounts for hospital and community demand, patient preferences over facilities and accommodation types, and threshold constraints on the number of alternative-level-of-care (ALC) patients in hospitals.
Due to the curse of dimensionality, an affine value function approximation is embedded into the MDP's linear programming formulation, yielding a tractable approximate linear program solved via column generation.
The model was validated on a case from the Ottawa region in Canada. Preliminary results indicate that proactive, preference-aware allocation policies can reduce ALC census while maintaining reasonable community wait times.