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

在许多公共部门中，系统管理者必须将有限的资源或服务能力分配给具有异构属性的候选人。由于公共资源（服务能力）的稀缺，候选人在获得资源（服务）之前必须经历很长时间的等待。系统管理员努力设计一个优先级规则，使总匹配效用最大化，这取决于候选资源和资源类型；与此同时，她可能还有其他目标要实现。例如，在许多公共系统中，希望在不同的候选类型之间保持公平的等待时间。研究以下服务体系：它们都可以被建模为具有一定优先级规则的多类队列，但每个队列都有其特殊性，这使得底层数学模型不容易分析。******1。自2008年以来，加拿大政府一直在积极寻求分配系统的建议，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，患者可能会为了等待高质量的器官而拒绝低质量的肾脏。因此，策略设计者的问题是寻找一种分配策略，使其达到具有最期望性能的纳什均衡。* * * * * * 2。急诊科(ED)***急诊科通常使用分诊系统将患者划分为优先级。然而，实际的路线决定主要取决于急诊科医生的个人决定。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病人在急诊科的路线。这个预测模型使我们能够优化医生的轮班安排，并预测等待时间，并在网站上发布给患者。******公共经济适用房分配***加拿大和美国为符合条件的低收入家庭、老年人、残疾人等提供经济适用房选择。例如，加拿大抵押和住房公司（CMHC）每年支持近60万户家庭。申请人需要在不同的住房类型中注明自己的偏好顺序。我们研究了最优排序机制，鼓励购房者如实报告自己的偏好，同时达到最优分配结果。******初级保健的随访预约管理***为了保持护理的连续性，家庭医生通常的做法是预留随访时间，以确保患者在规定的时间窗口内接受治疗。然而，提前预定座位与较高的不出席率相关，这得到了我们的实证研究结果的支持。我们研究了最优的优先顺序规则的随访，以尽量减少犹豫和未显示。* * * * *

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. *****