This paper presents a novel Mixed-Integer Nonlinear Programming (MINLP) model for a parallel-line Capacitated Lot-Sizing Problem (CLSP) with the sequence-dependent setup time/cost, due date, and preventive maintenance planning. The target of this integrated model is to specify optimal lot sizes, inventory, and shortage levels along with the optimal preventive maintenance plan and the best sequence, starting time, and completion time of the lots. The production and scheduling aspect of the problem is modeled as the CLSP with the sequence-dependent setup time/cost and due date, while maintenance sub-problem is modeled by using the time-based maintenance technique and age-reduction modeling concept with the actual run-time and Exponential lifetime distribution. For the complexity of the model, the MIP-based Rolling Horizon (RH) heuristic algorithms are developed to solve the linearized model in a reasonable truncated time. The computational results obtained from generated small- to large-sized instances show that the proposed RH1 and RH2 heuristic methods report the final solutions with better quality (lower relative gap and total cost) compared with the solutions reported by the truncated simple CPLEX method. Especially, the RH2 method provides a reasonable production plan, better-adjusted schedules with respect to the due dates, and a proper PM plan in comparison with the other solution methods. Also, the featured model develops an optimal production, scheduling, and maintenance plan with higher feasibility, more available production time, and lower total cost in comparison with the classic CLSP with the sequence-dependent setups that neglects the effects of sudden failures and corrective maintenance actions.