A sustainable dynamic closed-loop supply chain network equilibrium for collectibles markets

In this paper, we present a sustainable closed-loop supply chain network equilibrium problem for collectible items in a time-dependent framework. In particular, we consider a network consisting of manufacturers, retailers, demand markets, and an online second-hand platform involved in forward and reverse logistics competition. Manufacturers as well as retailers try to control the amount of emissions generated in transaction processes. We analyze the optimal behaviors of all the decision-makers, and we give the governing closed-loop supply chain network equilibrium conditions. Then, we introduce the associated evolutionary variational inequality and the related infinite-dimensional projected dynamical system, which are convenient to solve such a problem. Finally, using a discrete-time approximation procedure, we solve a numerical example considering eBay as online platform.