Abstract
This paper constructs a continuous dual-channel closed-loop supply chain (DCLSC) model with delayed decision under government intervention. The existence conditions of the local stability of the equilibrium point are discussed. We analyze the influence of delay parameters, the adjustment speed of wholesale price, recovery rate of waste products, direct price, carbon quota subsidy, and carbon tax on the stability and complexity of model by using bifurcation diagram, entropy diagram, attractor, and time series diagram and so on. Besides, the delay feedback control method is adopted to control the unstable or chaotic system effectively. The main conclusions of this paper show that the variables mentioned above must be within a reasonable range. Otherwise, the model will lose stability or enter chaos. The government can effectively adjust manufacturers' profit through carbon tax and carbon quota subsidy, and encourage manufacturers to reduce carbon emissions and increase the remanufacturing of waste products.
Highlights
The rapid development of the Internet has increased people’s shopping choices, and nowadays online shopping and physical stores coexist, so this paper studies closed-loop supply chain (CLSC)problems against the background of dual-channel retail availability
We find that scholars mainly discuss carbon emissions, carbon tax and government subsidies in dual-channel supply chains or the CLSC
We are more concerned about the following aspects: (1) the game behaviors of product sales and recycling in dual-channel closed-loop supply chain (DCLSC) are studied; (2) manufacturers sell new products and remanufactured products through direct channel and retailer channel, respectively; (3) the government encourages manufacturers to recycle and remanufacture waste products by using carbon quota subsidies and carbon tax policy simultaneously; (4) manufacturers and retailers adopt postponement strategies when making price decisions; (5) the influence of parameters on the stability and complexity is analyzed based on entropy theory and nonlinear dynamics theory; (6) the chaotic system is effectively controlled by using the method of delayed feedback control
Summary
The rapid development of the Internet has increased people’s shopping choices, and nowadays online shopping and physical stores coexist, so this paper studies closed-loop supply chain (CLSC). We are more concerned about the following aspects: (1) the game behaviors of product sales and recycling in DCLSC are studied; (2) manufacturers sell new products and remanufactured products through direct channel and retailer channel, respectively; (3) the government encourages manufacturers to recycle and remanufacture waste products by using carbon quota subsidies and carbon tax policy simultaneously; (4) manufacturers and retailers adopt postponement strategies when making price decisions; (5) the influence of parameters on the stability and complexity is analyzed based on entropy theory and nonlinear dynamics theory;. The influence of various decision main contributions of this paper areand as follows: first, we construct a dual-channel closed-loop critical parameters on the dynamic behaviors of supply chain system are analyzed, such as supply chain model with time delay based on government intervention, and discuss the price decision bifurcation, and entropy.
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