The complexity analysis and chaos control in omni-channel supply chain with consumer migration and advertising cost sharing

Abstract Based on omni-channel retailing, considering consumer migration and advertising cost sharing, this paper builds a dynamic price and advertising game model of omni channel supply chain with BOPS (buy-online-pickup-in store). Based on game theory and chaotic dynamics theory, we analysis equilibrium points and local stability of the system. Besides, we focus on the stability and complexity of the system with respect to adjustment parameters, the migration rate of the online consumer (MROC), the migration rate of traditional consumer (MRTC) and advertising cost sharing rate (ACSR). These factors are discussed by numerical simulation. Such as 3D stable region, attraction basins and bifurcation diagram. Results show that over high adjustment parameter, MRTC and ACSR lead the system to lose control and show complexity behaviors. As the system go into a chaotic state, the profits of manufacturer and retailer tend to decline. Finally, because of the effects of chaos, the paper proposes the feedback control method to control efficiently the chaotic system. The results provide some managers with relevant management insights in an omni-channel supply chain.