Equilibrium in supply chain network with competition and service level between channels considering consumers' channel preferences

This paper considers a dual-channel supply chain network consisting of multiple competing manufacturers, multiple competing retailers and multiple demand markets. Each manufacturer produces and distributes his products via direct e-commerce channel along with traditional physical channel. The manufacturers also provide services for the consumers in both channels, while the retailers only offer offline services to the consumers. On this basis, a dual-channel supply chain network equilibrium model with pricing and service decisions are established based on variational inequality theory. Nash equilibrium solutions are obtained by modified projection and contraction method. Combined with numerical examples, we analyze the impact of three critical factors on the equilibrium states and profits. Some interesting managerial insights are derived. We find that the profits of the manufacturers decrease (increase) in the raw material conversion ratio under single channel case (dual-channel case), while the increase of the raw material conversion ratio always benefits the retailers and the whole dual-channel supply chain network; the service level in each channel is positively correlated with its transaction volume. There are significant inconsistencies among the best combinations of cross-channel price coefficients between two channels for the manufacturers, the retailers and the whole dual-channel supply chain network. The same equilibrium decision (service level, price) or profit may exhibit the opposite changing trend with respect to cross-channel price coefficients under two cases of active e-commerce transaction and inactive e-commerce transaction. When the introduction of e-commerce channel can bring more profits for the whole dual-channel supply chain network, the manufacturers should provide reasonable allocation schemes of profit increment for the retailers to satisfy their participation constraints.