<p>A well-designed production schedule for cold rolling can enhance steel enterprises' operational efficiency and profitability. Nevertheless, the intricate constraints and numerous steps involved in cold rolling pose challenges to devising a rational scheduling plan. Therefore, considering the practical production constraints, this paper investigates a cold rolling scheduling problem for processing jobs with specific due dates and batch attributions on parallel heterogeneous machines with continuous production requirements. Firstly, the scheduling problem is formulated as a mixed integer linear program (MILP) model with an economic objective. Then, a modified genetic algorithm (GA) is proposed to search for the optimal solution to the MILP problem. Specifically, this method includes a heuristic initialization mechanism to generate feasible initial solutions, three heuristic mutation operators to generate promising candidate solutions, and a parallel computing mechanism to accelerate the evaluation process of the GA. The simulation results demonstrate that the proposed method can be effectively implemented to generate optimized scheduling schemes in the cold rolling process. </p>