In this paper, we study designing and managing effective dual-channel supply chain network equilibrium model to optimize the profit of each node in dual-channel supply chain network and satisfy seamlessly customer demand. The customer demand in each channel is driven by the heterogeneous consumer characteristic attributes. In our proposed model, Multinomial Logit (MNL) function is used to make a purchase decision for customers considering selling price, operation time and retail services. Furthermore, the Variational Inequality is used to express the equilibrium solution in dual-channel supply chain network. A numerical example in dual-channel supply chain network is presented to show the MNL function can be a good replacement for the demand function when customers are heterogeneous and the proposed model can be helpful to avoid time trap.