Scheduling consecutive days off: A case study of maritime pilots

Abstract Pilots are essential for the operation of maritime ports and an efficient piloting workforce management is critical to provide quality service to incoming vessels, to comply with the strict labor regulations associated with piloting and to avoid penalties due to delays in service. However, designing labor schedules that meet workforce demand and fulfill both labor requirements and workers’ preferences at once can become an arduous task. This paper presents two general days-on and days-off scheduling mixed integer linear programming models, which aim to configure extended breaks for each staff member. The first model produces schedules with two long breaks of bounded durations for each worker and minimizes the difference between the employees’ workloads. Having the option to modify the minimum lengths of each of the two types of breaks allows managers to comply with the workers’ desired rest patterns, while at the same time exploiting the flexibility gained by constraining the off-periods with a lower bound and achieving fair schedules in terms of break lengths and workloads. On the other hand, the second model assigns breaks as extended as possible and minimizes the difference between the rest accumulated by the workers. Its novel formulation allows maximizing the length of the workers’ breaks, an objective rarely found in the literature, and can be adjusted to prioritize the overall duration of the off-periods or the fairness of the distribution of breaks. Results of the application of these models to the piloting workforce in a Spanish port are shown, as well as a sensitivity analysis performed in order to assess the behaviour of the models when dealing with longer planning horizons and greater workforce sizes. Additionally, an ad-hoc model is developed for the assignment of special-maneuvering turns to the pilots.