The City of Toronto Long Term Care Homes & Services (LTCH&S) division is one of the largest providers of long-term care in the Canadian province of Ontario, providing care to 2,640 residents at 10 homes across Toronto. Our collaboration with LTCH&S was initiated to facilitate the increasingly challenging task of scheduling nursing staff and reduce high absenteeism rate observed among the part-time nurses. We developed a spreadsheet-based scheduling tool to automate the generation of schedules and incorporate nurses' preferences for different shifts into the schedules. At the core of the scheduling tool is a hierarchical optimization model that generates a feasible schedule with the highest total preference score while satisfying the maximum possible demand. Feasible schedules had to abide by a set of complex seniority requirements which prioritized more senior nurses when allocating the available shifts. Our scheduling tool was implemented in a 391-bed home in Toronto. The tool allowed nursing managers to generate feasible schedules within a fraction of an hour, in contrast to the status-quo manual approach which could took up to tens of hours. In addition, the schedules successfully accounted for preferences with on average above 94% of the allocated shifts ranked as most preferred.

中文翻译：

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优化可帮助计划多伦多市长期护理院的护理人员

多伦多市长期护理院和服务（LTCH＆S）部门是加拿大安大略省最大的长期护理提供者之一，为多伦多各地10所家庭的2640名居民提供护理。我们与LTCH＆S的合作旨在促进日趋艰巨的日程安排护理人员任务，并降低兼职护士中出现的高缺勤率。我们开发了基于电子表格的计划表工具，以自动生成计划表，并将护士针对不同班次的喜好纳入计划表。调度工具的核心是分层优化模型，该模型可生成具有最高总偏好得分并同时满足最大可能需求的可行调度。可行的时间表必须遵守一系列复杂的资历要求，这在分配可用班次时会优先安排更多的高级护士。我们的调度工具是在多伦多拥有391张床的房屋中实施的。该工具允许护理经理在不到一小时的时间内生成可行的时间表，而现状的手动方法可能要花费数十个小时。此外，时间表成功地解决了偏好问题，平均优先级平均超过分配班次的94％。