Over the past 20 years, hospitals have seen a sharp rise in internal costs. These are the result of steadily growing patient numbers and the resulting increase in personnel requirements. Since approximately half of the costs incurred are generated by the hospital's staff, there is a need for efficient staff planning to minimize personnel costs while maintaining a high level of service quality.
In practice, shift plans are currently often created by experienced physicians. On the one hand, this is very time-consuming and cost-intensive, and on the other hand, it often only delivers a result of average quality, since it is usually not possible for a human planner to take a large number of restrictions equally into account. These include, for example, aspects relating to fairness and equality within the workforce, as well as labour law regulations such as the planning of break and rest periods and the guarantee of the maximum permitted working hours. In this context, software-based mathematical optimization through models offers the possibility of generating plans that take into account the rules to be considered within a short period. Plans generated according to mathematical models are of higher quality than those generated by hand since mathematical optimization can take into account a large number of differently weighted objectives simultaneously. This is not possible for a human.
The current state of research in the area of model-based workforce scheduling still offers room for improvement and expansion. One problem that has received little attention in research to date is the short-term rescheduling of physicians. Currently, senior physicians are busy every day finding replacements for physicians who are absent due to illness, for example. Automated rescheduling models can provide decision support by identifying the physician whose qualifications match those needed and whose rescheduling has the smallest impact on the overall plan.
Another problem in physician assignment planning is the long-term uniform distribution of fulfilled shift requests and assigned shifts. Previous models usually consider these metrics only for the current planning horizon. However, this can lead to some physicians being treated disadvantageously in the long run, as complete equality within only one planning horizon is rarely possible. Accordingly, a physician's request fulfilment rate or workload must be tracked and projected into the future. This allows the physician's priority in the planning process to be adjusted according to past data, and in the long run, a fair and even distribution can be achieved.
Due to the multitude of conditions that go into creating a plan, scheduling models are often very complex. This means that the creation of a plan can take up considerable computing time and computer resources. In this case, methods must be found for performing this calculation differently and therefore speeding it up. Heuristic methods are particularly suitable for this purpose, as they can produce valid plans in a reasonable amount of time. However, these plans are then not necessarily the best possible ones, but still sufficiently good to be used in practice.
Our research is concerned with the development of new methods that provide automated decision support for the scheduling of physicians in hospitals.
Professional and Vocational Training
The complexity of training increases in high-tech industries. As a result, apprenticeships are not only time-based but task-based. Predicting the exact number of procedures a trainee will be able to perform during these periods is not always possible. Accordingly, a trainee may not be able to perform all of the required procedures, and therefore delays in training may occur. An important aspect of the quality of an apprenticeship is that trainees need to know in advance what kind of tasks will be performed in the following periods and in which department they will take place. This is not only relevant for trainees, but also the personnel management. By having a given curriculum, management not only knows in advance who will be joining the department in the next period but can also assess the level of knowledge of the new trainee. Also, organizations should ensure compliance with the duration of the entire training. Especially in the context of work-life / family balance, a fixed duration of a training program is important. In addition, using the same curriculum for more than one trainee can increase the systematic nature of an apprenticeship. While trainees can compare their level with other trainees and share their experiences with younger trainees, the training manager is able to improve the skills of education due to the repetitive structure. Examples that include task-based apprenticeships include in-service training programs for physicians, such as those presented in our experimental study, police training, and also some smaller complex programs such as driver's license training.
Our research activities in this area focus on mathematical methods that allow us to quantify the benefits of flexibility about the assignments of further qualified nursing staff. Performance measures considered include, for example, fairness aspects such as the number of assigned weekend shifts and fulfilled staff requests, average staff utilization, and compliance with specified nursing ratios. Flexible nursing staff makes it possible to respond to fluctuations in nursing demand on different wards in a hospital by assigning them to different areas of deployment at short notice. If this flexibility is already taken into account in medium-term deployment planning, shift plans can be generated that are better suited to deal with unpredictable fluctuations in nursing demand.
In practice, we support, among others, the Hospital of Augsburg with the implementation of an Automated Duty Planning (ADP). ADP uses rule-based heuristics in the personnel management software to provide shift planners with (near) optimal monthly schedules. The quality of automatically generated duty schedules strongly depends on the initial configuration of priorities, employee qualifications and availability, and weighting of the different objectives in the duty schedule. Therefore, a precise adjustment of the data and input factors used in the daily operation of the ADP is required.
Furthermore, we deal with the nursing care planning in the emergency room of the Hospital Augsburg. Here, it is important to optimize shift design and scheduling for seasonal (hourly, daily, and monthly) fluctuations in patient volume. Inflexible shift planning with just a few shift types, such as "early shift," "late shift," and "night shift," can lead, for example, to enormous under- or overcoverage of nursing requirements, because the course of patient volume cannot be adequately reflected in personnel planning. This systematically results in times throughout the day when the nursing staff is over-utilized, while idle time is to be expected at other times of the day. With the help of mathematical optimization, additional shift types can be determined that ensure a more even utilization of staff.