Manufacturing algebra. Part I: modeling principles and case study Enrico Canuto 1 , Manuela De Maddis 2 , Suela Ruffa 2 1 Dipartimento di Automatica e Informatica, 2 Dipartimento di Ingegneria Gestionale e della Produzione Politecnico di Torino Torino, 1 1029 Italy {enrico.canuto, manuela.demaddis, suela.ruffa}@polito.it Abstract - 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. Index Terms -Manufacturing Algebra, discrete-event, state equations, manufacturing systems, modelling. I. I. INTRODUCTION The paper deals with the problem of modelling and controlling manufacturing systems. The proposed method is based on the mathematical framework offered by the Manufacturing Algebra (MA) and on discrete-event state equations as outlined in [1] and [2] . Manufacturing Algebra has been developed at the end of nineties, and since then for different reasons, .developments and applications have slowed down. This conference may be an occasion to review the algebra fundamentals, to test them through a simple case study in view of applications e.g. to the automotive industry. The algebra has been developed to model dynamics of production processes taking place in factories using mathematical objects and operations, at different degrees of accuracy and detail. It is conceived around a few concepts: 1) Direct relation with manufacturing. Algebra elements and their semantics are related with concepts and objects found in industrial manufacturing systems (Section III). 2) Separation principle. While manufacturing model describes the materials flows and the operations that occur during the manufacturing process of each product, factory model describes the physical layout, accounting for machines, transport means and storage places. Both models are kept as separate entities, but their link is defined and formulated (Section V.A) 3) Aggregation principle. The principle states that lower- level entities can be combined to provide a reduced number of higher-level entities having the same properties of the lower-level. 4) Multilayer modeling. The manufacturing process is described at different levels of detail in an incremental way, based on the aggregation principle. 5) Hierarchical control. Control units are part of the model of the manufacturing system and are compatible with the multilayer architecture of the model. The result is a hierarchical control scheme. Previous work on manufacturing algebra has been already published, see [3] , [4] and [5] . Here, the main concepts of the algebra are recalled and referred to a simple case study, by reducing the formal burden and avoiding formal proofs. The following problems are treated: how to describe a manufacturing process (Section IV) and how to link this description with the factory layout (Section V). How to simplify models using the aggregation principle, how to obtain a multilayer model, how to design control strategies are treated in a companion paper [19] . Several methods for modelling and controlling manufacturing systems have been proposed. A comprehensive discussion is in [6] . Several textbooks are available: relations to and discrepancies from [7] will be outlined. The need for a flexible, self-programmable, closed-loop and distributed technique to design and implement complex manufacturing operations seems still an open problem [8] . Proposed solutions are usually in the form of software architectures and packages (for simulation, monitoring and control) [9] , empirical approaches [10] or network structures [11] , and usually do not stem from a formal and comprehensive mathematical background, unless they are based on well known formal methods such as Petri Nets [12] , or approximate decomposition techniques and Markov models. Problems of distributed scheduling [13] , parts routing [14] , service rate selection have been extensively studied, though explicit solutions can be hardly achieved [15] [16] [17] . Since 1536 978-1-4673-1277-6/12/$31.00 ©2012 IEEE Proceedings of 2012 IEEE International Conference on Mechatronics and Automation August 5 - 8, Chengdu, China