In workforce scheduling for emergency medical services, it is important to ensure sufficient coverage at all time. Thus, planning has to consider unpredictable employee absences. To hedge against this type of uncertainty, on-call duties can be assigned to employees. In practice, these are often assigned ex-post based on the regular schedule. Little literature on workforce scheduling for ambulances or the planning of on-call duties exists. We present new set covering based integer programming formulations for cyclic stint-based staff scheduling with on-call duties. It is desirable for employees to work on consecutive days, called a stint, with a subsequent recovery period. On-call duties can be individually scheduled in-between two stints. Our model formulations integrate different cycle times for regular and on-call duties. A simple schedule that repeats quickly is devised for regular duties, while the on-call duty schedule rotates after each cycle to ensure fairness. The proposed models are applied to a local German emergency medical services provider. Using our stint-based model formulations, the planning complexity has been greatly reduced and reasonably large problem instances can be solved to optimality. Employee preferences, such as fairness, less work on weekends and longer recovery times, were taken into account to a high degree.

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