Online rescheduling of physicians in hospitals

Abstract

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 manages to respect interdependencies between duty and workstation roster whereas the sequential models will always optimize for the plan which is created first. Overall, results indicate that our integrated model parameters allow managing the trade-off between plan quality goals and plan stability.

Appendix

See Tables 2, 3, and 4.

Table 2 Demand ${\bar{d}}^{\text {duty}}_{it}$ for overnight duties

Table 3 Demand ${\bar{d}}^{\text {duty}}_{it}$ for 4-day late duties

Table 4 Maximum (${\bar{d}}^{\text {station}}_{ht}$, upper row) and minimum ($\underline{d}^{\text {station}}_{ht}$, lower row) demand of workstations h