Network-based Models for Scheduling under Uncertainty

在日常服务中，调度问题通常涉及事先未知的数量。例如，当医疗诊所为病人安排一次预约时，无法确定这次预约需要多长时间，或者之前安排在当天的预约是否会比最初预期的时间更长。过于乐观的时间表，并假设患者就诊时间短，可能会导致不希望的患者等待时间。相比之下，在预约时间上允许太多的灵活性可能会导致医生空闲，每天在诊所看病的病人数量减少。类似的场景也出现在大量其他应用程序中，例如在安排包裹递送、云服务中的工作、共享经济应用程序中的乘车以及呼叫中心的服务请求时。随着数据分析的进步，我们现在可以利用大量的数据来准确地模拟这种不确定性。机器学习和统计方法变得越来越容易获得，允许从业者更容易地获得准确的概率分布或构建复杂的模型来预测，例如，患者预约时间。然而，利用这些信息来设计更好的调度的优化模型是出了名的难以解决。这些模型将复杂的不确定性结构与一系列特殊约束相结合，严重限制了它们在实践中的适用性，并提出了新的理论和计算挑战。在这些挑战的激励下，我的建议将为不确定参数下的调度开发新的优化方法。研究的重点是基于不确定性的网络编码的另一种建模视角。具体来说，网络是灵活的数据结构，可以紧凑地表示大量信息，例如未知变量的未来结果集。它们可以与数学规划和最先进的优化技术结合使用，以更有效地获得更好的时间表，为预测和规范分析提供新的桥梁。该建议侧重于调度挑战，其中网络模型具有独特的方法优势，例如基于场景的方法，集成机器学习/优化模型和随机动态程序。特别是，将使用与国家和国际组织合作的真实数据集来评估结果。其结果是一系列计算实用工具，决策者可以使用这些工具来增强医疗保健、运输和物流等方面的调度服务。通过这一提议和对高素质人才的培训，我们的目标是将加拿大定位在以数据为导向的循证管理的前沿，特别是通过开发下一代分析工具，通过优化和严格的方法提取数据的价值。

In day-to-day services, scheduling problems often involve quantities that are unknown in advance. For example, when a medical clinic schedules an appointment for a patient, it is uncertain as to how long the appointment will take, or if previous appointments scheduled for that day will run longer than initially anticipated. Schedules that are overly optimistic and assume short patient visits may lead to undesired patient waiting times. In contrast, allowing too much flexibility on appointment lengths can result in idle physicians and a reduced number of patients seen daily at the clinic. Similar scenarios occur in a large array of other applications, such as when scheduling parcel deliveries, jobs in cloud services, rides in shared-economy apps, and service requests in call centers. With the advancement of data analytics, we can now exploit large amounts of data to accurately model this uncertainty. Machine learning and statistical methods have become increasingly more accessible, allowing practitioners to more easily derive accurate probability distributions or to construct sophisticated models to predict, e.g., patient appointment lengths. However, optimization models that leverage this information in order to design better schedules are notoriously difficult to solve. Such models combine complex uncertainty structure with a range of idiosyncratic constraints, severely limiting their applicability to practice and presenting novel theoretical and computational challenges. My proposal, motivated by these challenges, will develop novel optimization methodologies for scheduling under uncertain parameters. The focus of the research is on an alternative modeling perspective based on network encodings of the uncertainty. Specifically, networks are flexible data structures that can compactly represent large amounts of information, such as the set of future outcomes of an unknown variable. They can be used in conjunction with mathematical programming and state-of-the-art optimization techniques to derive better schedules more efficiently, providing new ways to bridge predictive and prescriptive analytics. This proposal focuses on scheduling challenges where network models present unique methodological benefits, such as in scenario-based approaches, integrated machine learning/optimization models, and stochastic dynamic programs. In particular, results will be evaluated using real datasets from collaborations with national and international organizations. The outcome is a series of computationally practical tools that decision makers can use in order to enhance scheduling services in healthcare, transportation, and logistics, to name a few. With this proposal and the training of high-qualified personnel, we aim to position Canada at the forefront of evidence-based management as driven by data, specifically by developing the next generation of analytical tools that extract the value of data through optimization and rigorous methodologies.