State-variable modeling for healthcare planning and scheduling

2017年，加拿大卫生预算总额为2420亿美元，占加拿大国内生产总值(GDP)的11.5%。在医疗保健系统中有效的决策非常关键，可以带来显著的节省。医疗保健系统中的多个不确定性来源是做出有效决策的主要挑战之一。从这个角度来看，能够有效地解决随机优化问题是至关重要的。该研究项目为不确定情况下的决策开发了新的随机优化模型，并将其应用于医疗保健计划和调度问题。在此背景下，我们将在考虑各种不确定因素的情况下，对手术室规划和调度、门诊预约调度以及放射性药品生产和交付的调度进行研究。 手术室计划与调度(ORPS)是医院最重要的决策问题之一，占医院年度预算的40%以上。门诊预约排程(OAS)也是医疗操作排程的另一个重要实例，它对于有效利用医生和用于诊断测试(例如CT扫描、MRI扫描、超声)的设备等人力医疗资源非常关键。文献中的现有模型只能解决非常简化的随机版本的ORPS和OAS问题。这项研究计划提出了更有效的随机优化模型，能够解决具有指数数量的随机场景的相当大的实例。所提出的模型将同时解决这些问题中的许多不确定因素，如手术持续时间和患者在ORPS病房的恢复时间的不确定性，以及就诊时间、患者到达时间的不确定性，以及OAS中未出现的可能性。 我们还考虑了放射性药物成像中的时间安排，这是诊断骨骼问题的一种先进技术。它的市场规模为35亿美元，预计到2023年将增加到52.6亿美元。从管理的角度来看，生产和交付放射性药物的最佳时机非常关键，因为它们是昂贵的材料，寿命非常短，以指数速度恶化。最先进的方法主要是确定性模型，忽略了不同的不确定性来源。在这个研究方向，我们将提出新的随机优化模型，以解决各种不确定性，如随机时间依赖的旅行时间，由于注射引起的患者健康状况的变化导致成像持续时间的不确定性，以及未出现。

In 2017, the total health budget in Canada was $242 billion accounting for 11.5% of Canada's gross domestic product (GDP). Effective decision making in healthcare systems is very crucial and can result in significant savings. Multiple sources of uncertainty in healthcare systems is one of the main challenges to make effective decisions. From this perspective, it is essential to be able to solve stochastic optimization problems efficiently. This research program develops novel stochastic optimization models for decision making under uncertainty with applications in healthcare planning and scheduling problems. In this context, we will work on operating room planning and scheduling, outpatient appointment scheduling, and scheduling of production and delivery of radio-pharmaceutical by considering various uncertainty factors. Operating room planning and scheduling (ORPS) is one of the most important decision making problems in hospitals that accounts for more than 40% of their total annual budget. Outpatient appointment scheduling (OAS) is also another important instance of healthcare operations scheduling that is very critical for the efficient use of human medical resources such as physicians and equipment for diagnostic tests (e.g., CT-scan, MRI-scan, ultrasound). Available models in the literature can only solve very simplified stochastic versions of the ORPS and OAS problems. This research program proposes significantly more effective stochastic optimization models that are capable of solving considerably larger instances with an exponential number of stochastic scenarios. The proposed models will simultaneously address many uncertainty factors in these problems such as uncertainty in surgical durations and recovery times of patients in wards for ORPS and uncertainty in visit times, patients' arrival times, and the possibility of no-shows in OAS. We also consider scheduling in radio-pharmaceutical imaging that is an advance technology in diagnosing bone issues. It has a market of $3.5 billion that is predicted to increase to $5.26 billion by 2023. From a managerial viewpoint, optimal timing for production and delivery of radio-pharmaceuticals is very critical as they are expensive materials with very short life deteriorating in exponential rates. The state-of-the-art approaches are mainly deterministic models ignoring different sources of uncertainty. In this research direction, we will propose novel stochastic optimization models addressing various uncertainties such as stochastic-time-dependent travel times, uncertainty in imaging durations due to the change in the health's situations of patients because of the injection, and no-shows.