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New Methods for Resolving Conflicting Requests with Examples from Medical Residency Scheduling

机译：解决示例中的冲突请求的新方法

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In scheduling medical residents, the objective is often to maximize resident satisfaction across the space of feasible schedules, relative to the many hard constraints that ensure appropriate patient coverage, adequate training opportunities, etc. A common metric of resident satisfaction is the number of time-off requests that are granted. Simply maximizing this total, however, may lead to undesirable schedules since some requests have higher priority than others. For example, it might be better to grant one resident's request for a family member's wedding in place of two residents' requests to attend a rugby game. Another approach is to assign a weight to each request and maximize the total weight of granted requests, but determining weights that accurately represent residents' and schedulers' preferences can be quite challenging. Instead, we propose to identify the exhaustive collection of maximally feasible and minimally infeasible sets of requests which can then be used by schedulers to select their preferred solution. Specifically, we have developed two algorithms, which we call Sequential Request Selection Via Cuts (Sequential RSVC) and Simultaneous Request Selection Via Cuts (Simultaneous RSVC), to identify these sets by solving two sequences of optimization problems. We present these algorithms along with computational results based on a real-world problem of scheduling residents at the University of Michigan C.S. Mott Pediatric Emergency Department. Although we focus our exposition on the problem of resident scheduling, our approach is applicable to a broad class of problems with soft constraints.
机译：在安排医疗住院病人时，目标通常是在可行的时间表范围内使居民满意度最大化，这相对于确保适当的患者覆盖范围，适当的培训机会等诸多硬性约束。住院病人满意度的常用指标是时间关闭已批准的请求。但是，简单地最大化此总数可能会导致调度不理想，因为某些请求的优先级高于其他请求。例如，最好代替一位居民提出的参加一场橄榄球比赛的请求，来代替一位居民提出的参加家庭成员婚礼的请求。另一种方法是为每个请求分配权重，并最大化已批准请求的总权重，但是要确定准确代表住户和调度程序偏好的权重可能会非常困难。相反，我们建议确定最大可行和最小不可行的请求集的详尽集合，然后调度程序可以使用这些集合来选择其首选解决方案。具体来说，我们开发了两种算法，分别称为“通过割断顺序请求选择”（Sequential RSVC）和“通过割断同时请求选择”（Simultaneous RSVC），以通过解决两个优化问题序列来识别这些集合。我们根据密歇根大学莫特分校儿科急诊科调度居民的实际问题，提出了这些算法以及计算结果。尽管我们将重点放在居民调度问题上，但我们的方法适用于具有软约束的广泛问题。

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