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

在许多公共部门，系统管理员必须在具有不同属性的候选人之间对有限的资源或服务能力进行配给。在公共资源(服务能力)稀缺的情况下，考生在获得资源(服务)之前必须经历漫长的等待。系统经理努力设计一种优先规则，使总的匹配效用最大化，这取决于候选人和资源类型；同时，她可能还有其他目标要实现。例如，在许多公共系统中，希望在不同类型的候选人之间保持公平的等待时间。我们将研究以下服务体系。它们都可以被建模为配备了一定优先级规则的多类队列，但每种队列都有其特殊性，这使得底层的数学模型不容易分析。 1.已故捐赠者肾脏等候名单 自2008年以来，加拿大政府一直在积极寻找分配制度的建议，以改善移植结果，并为器官等待名单上的患者提供公平的机会。使政策设计问题具有挑战性的是，患者可能会拒绝低质量的肾脏供应，以等待高质量的器官。因此，策略设计者的问题是寻找一种分配策略，这将导致具有最期望性能的纳什均衡。 2.急诊科 急诊室通常使用分诊系统将患者分类为优先级。然而，实际的路径选择主要取决于急诊医生的个人决定。通过分析急诊科医生的历史决策模式，我们开发了一个模型来预测患者在急诊室的路径。这个预测模型使我们能够优化医生的轮班时间表，并预测等待时间，并在网站上发布给患者。 3.公共经济适用房编配 加拿大和美国为符合条件的低收入家庭、老年人、残疾人等提供负担得起的住房选择。例如，加拿大抵押贷款和住房公司(CMHC)每年支持近60万户家庭。住房申请者需要明确他们在不同住房类型中的优先顺序。我们研究最优的排名机制，鼓励申请者如实报告自己的喜好，同时获得最佳的分配结果。 4.管理初级保健的后续预约 为了保持护理的连续性，家庭医生的通常做法是为后续探视预留时间，以确保这些患者在规定的时间窗口内得到护理。然而，提前预定一个时段与较高的缺勤率相关，这一点得到了我们的经验发现的支持。我们研究了后续访问的最优优先级规则，以最大限度地减少停顿和缺勤。

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.