In real-life production environments it is often the case that the processing of a task on a given machine requires the assistance of a human operator specially skilled to process that task. In this paper, we tackle a scheduling problem involving operators that are skilled to manage only subsets of the whole set of tasks in a given shop floor. This problem was recently proposed motivated by a handicraft company. In order to solve it, we make some contributions. We first propose a general schedule builder and particularize it to generate several complete solution spaces. This schedule builder is then exploited by a genetic algorithm that incorporates a number of problem-specific components, including a coding schema as well as crossover and mutation genetic operators. An experimental study shows substantial improvements over existing methods in the literature and reveals useful insights of practical interest.