A dynamic equilibrium model of the oligopolistic closed-loop supply chain network under uncertain and time-dependent demands.

Highlights • A dynamic equilibrium model is constructed for the closed-loop supply chain network. • The demands and returns are uncertain and time-dependent. • Dynamic equilibrium condition is constructed by evolutionary variational inequality. • The equilibrium decisions are strongly affected by the time-dependent demands. Abstract In this paper, we develop a dynamic equilibrium model of oligopolistic closed-loop supply chain network to account for the seasonality of demand. In this model, demands and returns are uncertain and time-dependent. The dynamic Cournot-Nash equilibrium of the oligopolistic network is constructed by evolutionary variational inequality and projected dynamical systems. The existence and monotonicity results are established and a computational method is developed for finding the dynamic Cournot-Nash equilibrium. Numerical examples are solved to illustrate the performance of our model. The results show that the firms' optimal production and transaction quantities are strongly affected by the time-dependent demands. [ABSTRACT FROM AUTHOR]