Optimized planning of nursing curricula in dual vocational schools focusing on the German health care system

We investigate a problem in vocational school planning for nurses in countries with a dual vocational system, which closely combines theoretical and practical education and is highly regulated by federal legislation. The apprentices rotate through vocational school-blocks followed by assignments to hospital units, where they receive practical education. This program is regulated in high detail. Hospital units offer some slots for apprentices but expect just enough apprentices to be trained and educated. We create two mixed-integer programming models to optimally solve the underlying planning problems of (1) scheduling classes to theoretical and practical education blocks and (2) assigning apprentices to hospital units. The first model determines the number and length of school- and work-blocks on a class level, where its result is input to the second model, which finds individual unit-assignments for every apprentice fulfilling detailed curriculum requirements. Furthermore, it tries to exploit the units' educational capacities as well as possible. To solve the second model, we develop a heuristic decomposition procedure that enables good feasible solutions in short time. Our computational study is based on real-world data of our cooperation partner and provides valuable insights for management. The dataset consists of manually created schedules over the full 3-year program horizon and information on hospital units and their respective capacities. We test different parameter settings for our heuristic procedure and how they influence solution quality and runtime. Finally, we test, if students can be enabled to request individual vacations and evaluate benefits and drawbacks of different degrees of flexibility.