Coordination and control of multi-channel supply chain driven by consumers’ channel preference and sales effort

•A multi-channel Stackelberg dynamic game model is discussed in this paper.•Three kinds of key parameters are proved to effect on system stability significantly.•The complex dynamical behaviors and chaos control for system are investigated.•The complexity and profit of system under delay decision are studied in this paper. The Stackelberg Dynamic Game Model for a multi-channel supply chain which consists of one manufacturer and two retailers has been analyzed in this research as manufacturer provides a single product to traditional retailer, online retailer and direct channel. The complexity of the multi-channel system of such is therefore analyzed under the aid of the methods including stability domain, bifurcation diagram, the largest Lyapunov exponent, attractor, and time series. The results indicate that a great adjustment of supply order quantity in direct channels, retailer's order quantity, consumers’ channel preference, and sales effort will cause the system to lose stability and trap into complexity. On condition that customer didn't prefer the channel, the speed to adjust the order quantity would influence less on the system. Otherwise, when consumers’ channel preference too strong, the players on supply chain players would not see a profit increase, no matter how hard they'd improved their sales effort. And, so will it exhibit such a meagre influence on the profits of the whole supply players chain. During the period when sales efforts being adjusted, retailers, as the rule followers, will be confronted by more limitations than the rule maker the manufacturer. Then, to further analyze, parameters adjustment control method is utilized to control the chaos of the multi-channel supply chain. Furthermore, to investigate the influence of the delay decision on the stability domain and the profits. The research findings of this study can provide a great reference for managers and decision-making process in their supply chain management.