In the context of Industry 4.0, both of the ability to handle unexpected events and personalization customization are emphasized. This work investigates a parallel machine scheduling problem with uncertain skill requirements. The problem involves a two-stage decision-making process: (i) determining the workers’ skill training plan and the number of opened machines on the first stage before the realization of uncertain skill requirements, and (ii) scheduling jobs and assigning workers to jobs on the second stage, under known skill requirements. The objective is to minimize the expected total cost, including the workers’ skill training cost, machine opening cost and the expected penalty cost of jobs’ tardiness. A two-stage stochastic programming formulation is proposed, and an illustrative example shows the applicability of the model.