With the outbreak of the new coronavirus (Covid-19), many countries adapted mandatory mask policies to curb the spread of the virus. Even if some countries start to loosen the disposable mask requirements, mask policies are still mandatory at least during transportation and people are highly recommended to wear them in public spaces. Due to all these preventive mask policies, the demand for medical face masks has increased tremendously, and mask manufacturers began to take orders for varying types of masks in large quantities that have to be fulfilled within a short response time. Thus, it is significant for the manufacturer to schedule medical face mask production tasks as efficiently as possible. In this paper, disposable medical face mask production planning is studied when the orders have different release dates, due dates, and set-up times. The problem studied in this paper is motivated from a real-life mask manufacturer and a flow shop production scheduling problem is formulated with sequent two machines and set-up times while minimizing the total tardiness. A simulated annealing heuristic is proposed to solve this problem and we conclude that applying a simulated annealing heuristic results in a fast and efficient production plan.