Joint Design of Priority Rules and Service Capacity in Multi-class Queues and Applications in Public Sectors

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In many public sectors, the system manager has to ration the limited resources or service capacity among candidates with heterogeneous attributes. Given the scarcity of public resources (service capacity), candidates have to experience long wait before receiving the resource (service). The system manger strives to design a priority rule that maximizes the total matching utility that depends on both the candidate and resource types; meanwhile, she may have other objectives to achieve. For example, in many public systems, it is desirable to maintain equitable waiting times across different candidate types. We will study the following service systems. All of them can be modeled a multi-class queue equipped with a certain priority rule, but each has its specialty that makes the underlying mathematical model non-trivial to analyze. 1.Deceased-Donor Kidney Waitlist Since 2008, the Canadian governments have been actively looking for recommendations for an allocation system which improves transplantation outcomes as well as provide equitable access to patients on the organ waitlist. What makes the policy design problem challenging is that patients may reject a low-quality kidney offer in order to wait for high-quality organs. Therefore, the policy designer's problem is to search for an allocation policy, which leads to a Nash equilibrium with the most desired performance. 2.Emergency Departments (ED) EDs typically use a triage system to classify patients into priority levels. However, the actual routing decision mostly depends on the ED physician's individual decision. By analyzing the ED physicians' historical decision pattern, we developed a model to predict how patients are routed in EDs. This prediction model allows us to optimize the physician's shift schedule as well as to forecast the waiting time, which is released to patients on the websites. 3.Public Affordable Housing Allocation Canada and the U.S. provide affordable housing options for eligible low-income families, seniors, disabled, etc. For example, the Canada Mortgage and Housing Corporation (CMHC) supports nearly 600,000 households annually. The housing applicants need to specify their order of preference among different housing types. We study the best ranking mechanism which encourages house applicants to truthful report their preference and meanwhile achieves the best allocation outcome. 4. Management of Follow-up appointments in Primary Care To maintain continuity of care, a usual practice for family physician is to reserve slots for the follow-up visits to ensure that those patients receive care within the required time window. However, reserving a slot in advance is associated with a higher no-show rate, which is supported by our empirical findings. We investigate the optimal prioritization rule for the follow-up visits to minimize balkings and no-shows.