Manufacturing algebra. Part II: Aggregation, control and simulation

A few formal entities for modeling manufacturing processes and factories have been outlined in a companion paper of this conference. The link between a manufacturing model and its implementation in a factory plant has been formulated by ordering object drawing and delivery in a sequence of events, and by scheduling their starting time. Real-time simulation is then viable by providing the production units with a sequence of operations to be performed together with their starting times: simulation may be referred to as the direct problem. Nothing has been said about the synthesis of command sequences from higher-level production orders listing quantities of finished products to be delivered at certain times. The problem, which may be referred to as the inverse problem, is treated in the paper with the help of aggregation/disaggregation concepts and procedures. They allow to formulate the order sequence as a higher-level command sequence dispatched to the higher-level production unit in charge of the whole factory. The higher level command is then real-time disaggregated into lower-level commands (push). The status of the lower-level units is in turn transmitted to higher-level units (pull) for building-up their aggregated status. Simulation results of the factory model driven by the designed real-time control are provided.