Manufacturing algebra. Part I: Modeling principles and case study

Manufacturing Algebra provides a set of mathematical entities together with composition rules, that are conceived for modeling and controlling a manufacturing system. In this first paper, only the modeling capabilities are outlined together with a simple case study. Though the algebra is formally introduced, the scope of the paper is to familiarize the reader with the proposed methodology, and to highlight some peculiarities. To this end formulation is reduced to a minimum and no theorem is included. Among the algebra peculiarities, both manufacturing process and the factory layout are neatly defined in their basic elements, and the link between them is given. A manufacturing model (parts, operations) need to include time and space coordinates in order it could be employed by factory elements like Production Units and Control Units. This asks for the definition of event and event sequence and of the relevant discrete-event elements and operators. A further peculiarity to be clarified in the second part, is the capability of aggregating algebra elements into higher level components, thus favoring hierarchical description and control of manufacturing systems.