Complexity analysis of the dual-channel supply chain model with delay decision

In the oligopoly e-commerce market, the oligarch retailers sell products through traditional channel, while others through both network and traditional channel in order to obtain greater profits. Instead of discussing classic Bertrand game model, which past studies have done, we considered dual-channel retailer who makes price decision through both in network channel and traditional channel. This paper used the bifurcation theory of dynamical system, considering dual-channel retailer who makes delay decision. We performed a numerical simulation on system with different conditions, and some complex phenomenons occured, such as bifurcation and chaos. The results showed that adopting price delay decision in tradition channel would make the system more stable. While, adopting price delay decision in network channel makes the system less stable. When the market is in chaotic state, the using of delay decision would have an effect on the system stability in either traditional or network channels. The system become stable from chaos and would return to chaotic again with the increasing of weight in past period. Some interesting phenomenons happened when dual-channel retailer adopted delay decision in both channels. The superposition of delay decision would make the system more complex. At last, we measured the system's performance by using profit index. We analyzed the profits of different oligarchs when the system is in different states. When the system is in chaos, the total profits of the oligarchs are obviously less than that in a stable state. Adopting delay decision is a way to avoid profit loss when system is in chaotic period, but this requires the retailer has rich operational experience. That is because adopting delayed decision may not always enhance the competitive strength of oligarchs.