Fair shift change penalization scheme for nurse rescheduling problems

The nurse rescheduling problem denotes the problem of finding a new, feasible schedule when a disruption occurs during schedule operation. In most cases, rescheduling is needed when a nurse requires short-term absence and a substitution is essential to maintain care. Basically, rescheduling focuses on minimizing the shift changes between the current and the new schedule in order to best avoid disturbing the schedule operation and so prevent nurse dissatisfaction due to shift changes. Constraints within the nurse rescheduling problem may differ depending on the case. In this study, we develop a general optimization model that can be adjusted to various cases with different characteristics. The model incorporates a fair shift change penalization scheme, in which the type, timing and distribution of shift changes among nurses are taken into account. In addition, information from previous periods is considered, using an individual penalty score to distribute the shift changes fairly among the nurses. Based on the proposed penalization scheme and model, optimized schedules are generated in a short computational time for instances from literature, real-world based instances from a Portuguese hospital, and real instances from a care facility from Germany. The results of the computational study demonstrate the practical applicability of the approach. For most problem instances, the number of shift changes corresponds to the minimum number or deviates only slightly from it. At the same time, a much fairer distribution of these changes among nurses can be achieved.