Modeling closed loop supply chain system based on stochastic fuzzy Petri net

A new approach to model and analyze closed loop supply chain system is proposed based on Petri net theory. The approach proposed consists of two stages. In the first stage, the closed loop supply chain is modeled as a stochastic fuzzy Petri net model with conventional stochastic Petri nets in which the transition firing rates are characterized as fuzzy variables. In order to obtain the reachablility graph of the stochastic fuzzy Petri net, the fuzzy expected values of the transition firing rates are calculated and the stochastic fuzzy Petri net model is degenerated as a common SPN in the second stage. Then the degenerated Petri net is isomorphic to a continuous-time Markov chain. A numerical example analyzing the performance measure of closed loop supply chain system is given to show the effectiveness of proposed method.