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.

在医疗保健管理中，一个重要的问题是如何有效地分配容量有限的资源。从具有长计划视野的中央决策者的角度来看，许多医疗资源（例如预约空位，手术室和医院病床）都可以视为可重复使用的资源。受此观察结果的启发，我们研究了可重用资源对顺序到达的用户的分配问题的新版本。与之前有关可重用资源的工作不同，我们假设每个用户在需要做出决定之前都会告诉我们每个资源的预期使用持续时间。在用户根据特定分布随机到达的情况下，我们提出了一种基于最优值函数线性近似的算法，并表明，与在不同模拟中以及返回真实数据的案例研究中返回使用时间已知的情况下开发的通用方法相比，其性能要好得多。当用户按对抗顺序到达时，我们以示例的方式表明，很难设计出竞争比率较低的算法。由于用户实际上很少会按对抗顺序到达，因此我们提出的算法可用于有效地调度资源，例如医院中的预约空位和手术室。