This paper presents a continuous time optimization model for a dynamic pricing and inventory control problem in a dual-channel supply chain system. We consider a manufacturer’s redesign of traditional channel structures, based on customer behaviors, by engaging in direct Internet sales. While the manufacturer and its retailer set optimal pricing and inventory policies dynamically, this study considers both vertical integration and competition of two channels. For the former case, a continuous time optimal control problem is modeled, while for the latter a differential quasi-variational inequality (DQVI) formulation is applied to solve as a Cournot-Nash-Bertrand game. We provide implications for optimal strategies and note the effect of a customer acceptance index.