To Serve or Reserve? Managing Admissions in Systems Where the Condition of Customers Deteriorates

Problem definition: We study an admission control problem featuring two types of customers (urgent and non-urgent) and two groups of servers for urgent and non-urgent customers. A distinguishing feature of the system we consider is the possibility of the condition of non-urgent customers (requiring non-urgent servers) to deteriorate and to become urgent (and to require urgent servers). Deciding on whether to admit a customer is non-trivial because of the randomness in the customer arrival process, in the duration of service, and in the customer condition deterioration process and because of differences in the costs associated with not providing service for the two types of customers. In particular, the problem involves a complex trade-off between the benefit of admitting a customer of a particular type and the benefit of reserving server capacity, either for future customers or for current customers whose condition may deteriorate. The problem we study is motivated by admission decisions in healthcare settings. However, the problem and the results have broader applicability to other types of service systems such as call centers. Methodology: We formulate the problem as a Markov Decision Process over an infinite horizon. We use this formulation to determine the optimal policy. We show that this policy can be computed in polynomial time in the number of servers and we study its properties. Results: We show that the optimal policy generally does not admit a simple structure, and does not adhere to a simple priority. For example, it can be optimal to reject urgent customers even when urgent servers are available. It may also be optimal to reject urgent customers while admitting non-urgent ones even when both types of servers are available. However, we also show that conditions exist under which optimal admission is consistent with a strict priority policy and is characterized by a single threshold parameter. Managerial implications: Our findings highlight the importance of deploying a policy that carefully accounts for the subtle trade-offs between admitting urgent and non-urgent customers. Numerical results show that the optimal policy can significantly outperform other commonly used policies. We carry out a case study involving admission of COVID-19 patients at the National Centre for Infectious Diseases in Singapore. We show that, compared to the current approach, an optimal policy leads to an average of 7.36% reduction in inter-hospital patient transfers while maintaining the same level of throughput