A First-Order Hybrid Petri Net Model for Supply Chain Management

A supply chain (SC) is a network of independent manufacturing and logistics companies that perform the critical functions in the order fulfillment process. This paper proposes an effective and modular model to describe material, financial and information flow of SCs at the operational level based on first-order hybrid Petri nets (PNs), i.e., PNs that make use of first-order fluid approximation. The proposed formalism enables the SC designer to choose suitable production rates of facilities in order to optimize the chosen objective function. The optimal mode of operation is performed based on the state knowledge of the obtained linear discrete-time, time-varying state variable model in order to react to unpredictable events such as the blocking of a supply or an accident in a transportation facility. A case study is modeled in the proposed framework and is simulated under three different closed-loop control strategies. Note to Practitioners-The motivation of the present work is to provide a generic, simple and accurate model, able to integrate the material, financial and information flows description, for use by decision makers in SC management at the operational level. In particular, this paper proposes a model based on the first-order hybrid Petri net model formalism that provides SC designers with important key features. First, the model exhibits good computational efficiency and easy implementation in engineering software packages. Second, some SC design parameters, such as supplier and manufacturer production rates, are real continuous variables and can be determined by polynomial complexity optimization of suitable performance indices. Third, based on knowledge of the system state and information on the occurrence of typical operational unpredictable events (e. g., facility blockings and goods demands), the model enables the decision makers to update some operational design parameters in a closed-loop strategy. Future research aims to investigate on the decisional structure of the model in order to specify a decision support system based on the presented modeling framework.