Modeling and performance evaluation of supply chains using batch deterministic and stochastic Petri nets

Batch deterministic and stochastic Petri nets are introduced as a tool for modeling and performance evaluation of supply chains. The new model is developed by enhancing deterministic and stochastic Petri nets (DSPNs) with batch places and batch tokens. By incorporating stochastic Petri nets (SPNs) with the batch features, inhibitor arcs, and marking-dependent weights, operational policies of supply chains such as inventory policies can be easily described in the model. Methods for structural and performance analysis of the model are developed by extending existing ones for DSPNs. As applications, an inventory system and an industrial supply chain are modeled and their performances are evaluated analytically and by simulation, respectively, using this BSPN model. The applications demonstrate that our model and associated methods can solve some important supply chain modeling and analysis issues. Note to Practitioners-This paper was motivated by the problem of performance analysis and optimization of supply chains but it also applies to other discrete event systems where materials are processed in finite discrete quantities (batches) and operations are performed in a batch way because of batch inputs and/or in order to take advantages of the economies of scale. Existing Petri net modeling and analysis tools for such systems ignore their batch features, making their modeling complicated. This paper suggests a new model called batch deterministic and stochastic Petri nets (BDSPNs) by enhancing deterministic and stochastic Petri nets with batch places and batch tokens. Methods for structural and performance analysis of the model are developed. We then show how an inventory system and a real-life supply chain can be modeled and their performances can be evaluated analytically and by simulation respectively based on the model. The model and associated analysis methods therefore provide a promising tool for modeling and performance evaluation of supply chains.