Physicians are a scarce resource in hospitals. In order to minimize physician attrition, schedulers incorporate individual physician preferences when creating the physicians' duty roster. The manual creation of a roster is very time-consuming and often produces suboptimal results. Many schedulers therefore use model-based software to assist in planning. The planning horizon for duty schedules is usually a single month. Many models optimize the plan for the current planning horizon, without taking into account data on preference fulfillment and work load distribution from previous months. It is therefore possible that, when looking at a longer time horizon, some physicians are disadvantaged in terms of preference fulfillment more often than their peers, simply because this generates better results for the individual months. This may be perceived as unfair by the disadvantaged physicians. In order to eliminate this imbalance, we introduce a satisfaction indicator for preference fulfillment in physician scheduling. This indicator is computed for each physician on each monthly plan and is then used to inform decisions regarding preference fulfillment on the current and future plans. As a result, a more equal distribution of preference fulfillment among physicians is achieved. We run a computational study with three different update strategies for our satisfaction indicator. Our study uses 24 months of data from a German university hospital and derives additional generated data from it. Results indicate that our satisfaction indicator, combined with the right update strategy, can achieve an equal distribution of satisfaction over all physicians within a peer group, as well as stable satisfaction levels for each individual physician over a longer time horizon. As our main contribution, we identify that our satisfaction indicator is more effective in creating equal distribution of long-term satisfaction the higher the rate of conflicting preferences is.
Scheduling physicians is a complex task. Legal requirements, different levels of qualification, and preferences for different working hours increase the difficulty of determining a solution that simultaneously fulfills all requirements. Unplanned absences, e.g., due to illness, additionally drive the complexity. In this study, we discuss an approach to deal with the following trade-off. Changes to the existing plan should be kept as small as possible. However, an updated plan should still meet the requirements regarding work regulation, qualifications needed, and physician preferences. We present a mixed-integer linear programming model to create updated duty and workstation rosters simultaneously following absences of scheduled personnel. To enable a comparison with previous sequential approaches, we separate our model into two models for the duty and workstation roster which generate plans sequentially. In a case study, we apply our integrated and sequential models to real-life data from a German university hospital with 133 physicians, 17 duties, and 20 workstations. We consider a planning horizon of 4 weeks and reschedule physicians on each day for three different cost settings for the trade-off between plan quality (in terms of preferences, fairness, coverage and training) and plan stability, resulting in a total of 4201 model runs. We demonstrate that our integrated model can achieve near-optimal results with reasonable computational efforts. In each of these runs our model reschedules physicians within 1-21 s. We run the sequential models on the same data, but for only one cost setting, resulting in 1401 runs. The results indicate that our integrated model & Christopher N. Gross
Staffing hospitals 24 hours a day requires some physicians to be assigned to overnight duties via duty schedules. As overnight duties have an impact on physicians’ personal life, physicians can submit preferences indicating when they would prefer to perform duties and when they would prefer not to be assigned to a duty. The created schedule then tries to respect those preferences. However, some duties are assigned to physicians who have not requested them, simply because nobody requested these duties and they have to be covered. This workload should be evenly distributed. We propose a workload indicator that tracks how much duties physicians perform over several planning horizons. The workload from the past is then used to inform decisions on the current plan. Our workload indicator is integrated into a scheduling model for physicians in hospital. The application of our model to test data shows that our workload indicator helps to spread workload over all physicians more evenly.
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