Research On Supply Chain Network Equilibrium Model And Iterative Algorithm Based On Variational Inequality

The excessive emissions of carbon dioxide wreak havoc on the environment and the earth’s climate system.The carbon emissions trading market is a key tool to address climate change,and it is a powerful way for all countries to reduce greenhouse gas emissions and mitigate climate change.Obviously,the one-way supply chain that only focuses on economic benefits can no longer meet the needs of the current environment,and an increasing number of scholars are beginning to study the impact of carbon emissions on the close-loop supply chain decisions.In addition,when studying supply chain equilibrium models,they are often transformed into the form of variational inequalities and solved accordingly.Based on this,this thesis uses variational inequalities as a tool to establish a carbon emissions reward and punishment mechanism to actively promote corporate carbon emissions reduction work,and further study the solution algorithm of variational inequalities.The specific work is as follows:1.This thesis clarifies the inherent mechanism of the interaction between carbon emission factors and other factors,studies the closed-loop supply chain network equilibrium model.This thesis considers unit subsidy policies,introduces a carbon emissions reward and punishment mechanism,uses variational inequalities,establishes a multi-level closed-loop supply chain network model consisting of manufacturers,distributors,demand markets,and recycling centers,and analyzes the establishment conditions of the model.This thesis studies the problem of the global optimal solution of a closed-loop supply chain under carbon emissions constraints,explores the impact of the carbon emissions reward and punishment mechanism on the transaction volume,demand volume,carbon emissions volume,and member profits of the closed-loop supply chain,thereby verifying the effectiveness of the model.2.This thesis seeks to find the connection between variational inequality solution algorithms and iterative algorithms for closed-loop supply chain management models,and studies the numerical solution algorithm of variational inequalities.Based on the research of Censor and Thong,this thesis introduces an inertia term and constructs an inertia subgradient extragradient algorithm using fixed point theory and methods as tools The algorithm is used to solve the solution of bilevel pseudo-monotone variational inequalities in Hilbert space and only needs to project on the feasible set once.The strong convergence theorem is proved under mild assumptions.