Large-scale scheduling problems have remained difficult to solve despite the intense research in the area and many successful algorithms. In this paper, a new decomposition algorithm is presented which finds a good feasible solution even for large-scale problems in a reasonable time. In each iteration, a maximum allowed number of operations is first assigned to available units, then the algorithm alternates between a production quantity maximization step and a production time minimization step in each iteration. The performance of the "rolling operation" algorithm is illustrated using an industrial example.