In this paper we consider a supply chain network model with three tiers of decision-makers (manufacturers, retailers, and consumers) in the case when prices and shipments are evolving on time. Moreover, we assume that excesses of production and excesses of demand of the commodity are present. For such a framework we furnish, using the infinite dimensional duality theory, the equilibrium conditions for the representatives of each tier of the supernetwork, the time-dependent variational formulation governing the complete supply chain supernetwork, and we provide some existence theorems and a numerical example.