We consider two synchronized schedules in the supply chain (e.g., an assembly line schedule at a producing company and a supply schedule for a module). This is a multi-objective dynamic scheduling problem with constrained machine capacities. The optimization criteria include total lateness minimization and throughput maximization. Due to some random re-scheduling activities (i.e., new rush customer orders) at one of the companies, the schedule coordination should be performed again. This problem is a dynamic scheduling problem where machine capacities are constrained. If a machine is assigned to a new introduced job that came during the re-scheduling, it cannot be used for processing the initially planned jobs at the same time. This conflict should be resolved on the basis of new schedule coordination to execute both new and initial jobs. For such problem statement, a new dynamic model for coordinated scheduling of interlinked processes in a supply chain under partial re-scheduling is presented. The peculiarity of the proposed approach is the dynamic interpretation of scheduling based on a natural dynamic decomposition of the problem and its solution with the help of a modified form of continuous maximum principle blended with combinatorial optimization. The special properties of the developed model allow using methods of discrete optimization for the schedule calculation. Optimality and sufficiency conditions as well as structural properties of the model are investigated. Advantages and limitations of the proposed approach are discussed. With the developed approach, an explicit inclusion of a schedule changes in the SC coordinated decisions for a wide ranges of possible applications as well as a dynamic model and a tractable algorithm for optimal discrete time scheduling on the basis of continuous maximum principle have been obtained.