Batch deterministic and stochastic Petri nets modeling, analysis and its application to supply chain

Industrial systems are frequently characterized by batch processes where materials are processed in batches (finite discrete quantities) and many operations such as production, inventory replenishment, and distribution are usually performed in a batch way because of the batch nature of customer orders or in order to take advantages of the economies of scale. This brings in a need for new models which can describe and analyze the batch behaviors of these processes effectively. We recently introduced a new stochastic Petri net model called "batch deterministic and stochastic Petri nets" (BDSPNs) allowing the synchronization of discrete and batch token flows of the processes. In this work, the model is presented in a more formal way, its relevance to supply chain modeling is addressed, and its analysis methods are developed.