This thesis focuses on incorporating variability, specifically stochastic processing times, in the flexible job-shop scheduling problem. A metric called service level on the makespan (the date when all operations are completed) is used and motivated to evaluate the robustness of a schedule. This service level corresponds to the probability that the makespan is lower than or equal to a given threshold (typically one day or one week). Solution approaches are proposed and validated to determine a schedule that optimizes the proposed service level. These approaches rely on approaches from the literature for the deterministic problem and on scenario generation based on Monte-Carlo simulation. Many experiments have been conducted on new instances, which extend classical instances from the literature by considering that the uncertainty of the processing times is related to a job or to a machine. The numerical results make it possible to evaluate the impact of the critical parameters of the approaches, but also of the source of uncertainty (job or machine). The thesis concludes with various perspectives, in particular on the definition of other service levels than the service level on the makespan.