Modeling and Analysis of a Petri Net-Based System Supporting Implementation of Additive Manufacturing Technologies

The paper proposes a novel modelling and analysis technique of the system supporting implementation of additive manufacturing (AM) technologies specified by the interpreted Petri net. Nowadays, there is a need in a manufacturing enterprise to implement the new technologies supporting the realization of production, especially in terms of the possibility of unplanned crisis events. Managers expect such models to support their decisions in order to maintain or strengthen their competitive position thanks to the investments. Therefore, this paper proposes a system supporting the decision to implement AM technology, based on the interpreted Petri net, by utilizing its main advantages: the possibility of graphical modelling, and strong mathematical support of formal verification techniques. In particular, the proposed verification algorithm allows for detection of possible unbounded places. Contrary to the most popular analysis methods (which are bounded exponential in general case), it is proved that the presented technique is bounded by a cubic polynomial with the number of Petri net nodes. Finally, the presented modelling and analysis method is illustrated by a real-life case-study example of the decision-making model to support the implementation of AM technologies.
Note to Practitioners
—This paper is motivated by the limited performances in the existing modelling and analysis techniques of systems that support implementation of additive manufacturing (AM) technologies. In particular, the article proposes a system supporting the decision to implement AM technology, based on the interpreted Petri net. Existing approaches have important restrictions related to the exponential computational complexity of analysis methods. Therefore, verification of the model can be a real challenge to the designer. In contradistinction, the algorithm proposed in the paper permits the examination of the system in a polynomial time. The presented modelling and analysis ideas are illustrated by a real-life example of the decision-making system that utilizes implementation of AM technology. Managers of manufacturing enterprises, thanks to the use of the proposed approach, can assess the investment in AM technology in the following three unexpected situations: 1) delays in the delivery of materials and/or semi-finished products or the inability to receive materials and/or semi-finished products; 2) high employee turnover; 3) increasing costs of energy consumption. Thus, the application of this model allows for the harmonious conduct of manufacturing activities in conditions of unexpected situations.