An integrated multi-stage scheduling and routing problem with alternative machines at each supply chain (SC) stage and non-preemptive operations is studied. The peculiarity of the considered problem is the consideration of both continuous flows in operations and discrete assignments. Such problems are typical in the process industry. Taking into account the basic aspects that pertain to this case, a dynamic decomposition of the problem on the basis of optimal programme control is proposed. A particular feature and novelty of the presented study is the consideration of non-preemptive operations and their execution dynamics. The solution is based on a combined application of discrete and continuous optimization. With the special properties of the proposed scheduling model, it becomes possible to develop an optimal solution to the integrated scheduling and routing of jobs. Since the schedule generation is formulated in control terms, the models of scheduling and adaptation can be integrated. From the practical point of view, such integration can be advantageous subject to further dynamic analysis of the robustness, stability, and adaptability of SC schedules.