Dynamic planning with reusable healthcare resources: application to appointment scheduling

In healthcare management, one important problem is how to efficiently allocate resources with limited capacities. From the point of view of a central decision maker with a long planning horizon, many healthcare resources such as appointment slots, operation rooms, and hospital beds can be regarded as reusable resources. Motivated by this observation, we study a new version of the assignment problem of reusable resources to sequentially arriving users. Different from previous works on reusable resources, we assume that each user will tell us the intended usage duration of each resource upfront before a decision needs to be made. In the setting where users arrive randomly according to a certain distribution, we propose an algorithm based on linear approximations of the optimal value functions, and show that it performs better than common methods developed for the case where usage times are known upon return in different simulations, as well as in a case study with real data. When users arrive in an adversarial order, we show by example that it is hard to design an algorithm with a lower-bounded competitive ratio. As users are much less likely to arrive in an adversarial order in reality, our proposed algorithm can be used to effectively schedule resources such as appointment slots and operation rooms in hospitals.