Nurse scheduling is still an unsolved issue, as it is NP-hard and highly context-dependent. Despite this fact, the practice needs guidance on how to tackle this problem without using costly commercial tools. Concretely, we have the following use case: a Swiss hospital is planning a new station designed for nurse training. The capacity planning is finished, and the hospital wants to assess whether shift planning with known constraints leads to valid solutions. Here, a mathematical model is combined with a genetic algorithm. We trust the solution of the mathematical model more, but if it does not provide a valid solution, we try out an alternative. Our solutions indicate that actual capacity planning together with the hard constraints cannot lead to valid staff schedules. The central conclusion is that more degrees of freedom are necessary and that open-source tools OMPR and DEAP are valuable alternatives to commercial products such as Wrike or Shiftboard, in which the degree of freedom of customization is reduced in favor of easiness of use.
Keywords: Mixed-integer programming; genetic algorithms; staff scheduling.