A plethora of contributions have appeared in the literature over the past decade in the area of production planning of a single machine with sequence-dependent changeovers. Most of them, however, deal with the deterministic optimization model where all the parameters are considered known, which render optimal schedules, sub-optimal, or even infeasible in practice. In this paper, we first develop a new deterministic model based on a hybrid discrete- and continuous-time mixed-integer linear programming model for the production scheduling of a single machine with sequence-dependent changeovers. The proposed model (i) considers a time interval in which the processing machine is unavailable due to some maintenance jobs, and (ii) monitors inventory levels over shorter time scales, rather than at the end of predefined long-term periods. Then, the robust counterpart of the deterministic model is devised using the Γ-robustness approach that considers uncertainty in processing and changeover times. The objective is to find robust production schedules such that the sum of holding and changeover costs is minimized. We demonstrate the performance of the proposed model with a real-world case study.