With the increasing demand for customization, flow shop scheduling tends to process multi-variety small batch products. Thus, there are frequent switches between batches. Frequent switchovers between different sets are required during batch changeover, where machine setups may be necessary. This paper investigates scheduling optimization and work-in-process inventory optimization problems in a hybrid flow shop with rolling processing requirements. Developing continuous processing conditions to meet rolling processing requirements presents a significant challenge. In this work, continuous processing conditions are derived. Subsequently, a linear programming model is designed to find an optimal solution for this scheduling problem. Formulas for calculating work-in-process inventory are presented. To enhance work-in-process storage, a greedy algorithm with bubble sort and a Q-learning algorithm with a modified ε-policy are proposed to find an optimized product sequence and reduce work-in-process inventory, respectively. Numerical experiments evaluate the effectiveness and efficiency of the proposed methods.