Dynamic Resource Allocation in a Hierarchical Appointment System: Optimal Structure and Heuristics

To better manage patient flows, China has promoted a referral system across the country. Patients are encouraged to receive the initial diagnosis in community hospitals (CHs), and general hospitals (GHs) manage a slot reservation process to fulfill the needs of referral patients, who are in more severe conditions. According to the system practices, however, the reservation policy usually leads to either underutilized resources or unsatisfied referrals. This article aims to investigate a more effective method of allocating resources in GHs. We formulate the referral system as an appointment booking problem, considering the notion of the patient mix and system dynamics. The decision process of the referral system is captured by a discrete-time finite-horizon Markov decision process (MDP) model under a general framework. Theoretically, we analyze the structural properties of the MDP value functions to prove the monotonic properties of the optimal dynamic policy. The properties inspire us to design a heuristic policy called advanced referrals (ARs) policy, which offers resources to high-priority referrals earlier than regular patients. We prove that the AR policy is asymptotically optimal with infinite capacity and demand rates. Finally, we compare the performance of the AR policy with the optimal dynamic policy in numerical experiments, and also show that our policy outperforms fixed-reservation and first-come-first-serve policies which are widely used in practice. Note to Practitioners-In recent years, the healthcare system in China has been implementing the policy that general hospitals (GHs) reserve a fixed amount of slots for referrals from community hospitals (CHs), encouraging patients to choose CHs for initial diagnosis. However, the reservation policy ignores the demand uncertainty and system dynamics, which leads to circumstances where the reservations are either insufficient or underutilized most of the time. In the case of insufficient reservations, referrals will experience a treatment delay, while the underutilized slots lead to wastes of resources. In this work, we propose a more effective method that optimizes the allocation of GH resources between referrals and nonreferrals. In addition to analyzing the structure of the optimal dynamic policy, we design a heuristic policy that allows referrals to acquire resources earlier in time. This heuristic policy decides on a block time for the regular patients, and before the block time regular patients are not allowed to access the system, while referrals can get access to the resources freely. This policy is easy-to-implement and can better manage demand uncertainty. We provide an approach to calculate the policy and validate its performance both theoretically, and numerically.