Study On Multi-period Closed-loop Supply Chain Equilibrium Under Brittleness Of Complex System

With the progress of science and technology,the market competition,globalization and the increasing personalization of the market demand,the competition among enterprises is gradually changing to the supply chain competition.The closed-loop supply chain has advantages in saving resources,enhancing the competitiveness of enterprises and providing value-added services to consumers,so the closed-loop supply chain emerges as the times require.But because it involves more participants and links,increase the uncertainty and complexity of the research,in order to carry out more effective management,to better guide the participants' decision,but also to avoid the participants to pursue their own interests as the goal while ignoring the overall revenue of the closed-loop supply chain,need to solve the equilibrium of the system.Therefore,this paper studies the closed-loop supply chain system from the perspective of complex system and brittleness theory,which has important theoretical significance and practical value.Firstly,this paper introduces the research background and significance of the paper,analyzes the deficiencies existing in the related fields at home and abroad,and puts forward new research directions.Furthermore,the research content,technical route and research method of this paper are given.On this basis,in the process of this paper use the theory of knowledge are introduced,including the theory of complex system brittleness,the basic structure of closed-loop supply chain,the related theory of variational inequality and the solution of system equilibrium,etc.Secondly,a preliminary closed loop supply chain structure is proposed,from the perspective of brittleness of complex system,the degree of brittleness as a whole show to the world is measured by using entropy theory.When the overall degree of brittleness of the closed-loop supply chain system exceeds the threshold,resulting in the collapse of the system,how to weak the brittle relationship between systems while reducing the overall brittleness of the system,so as to maintain the stability of the system.By analyzing the structure and characteristics of the closed-loop supply chain system,the brittle propagation model is established,and the hierarchical brittleness diagram of the system is obtained,and the brittle source of the closed-loop supply chain system is found out.This paper gives a concrete solution to the brittle source and is used to improve the closed-loop supply chain system.Putting forward from the origin of the brittle source,combining with brittleness linkage entropy and brittleness correlation coefficient to find the largest subsystem associated with brittle source,for the brittle source with cracking,merging or deleting a series of measures to reduce the system brittleness.Thirdly,this paper studies the closed-loop supply chain composed of multiplesuppliers,manufacturers,retailers,demand markets and recyclers,combining with the dynamic situation of multi-planning period in the real closed-loop supply chain from the perspective of system brittle risk,the equilibrium model is established for each participant to pursue its own profit maximization,and the brittleness risk function is introduced.The brittleness degree of the system is used to measure the probability of brittleness risk.Using the variational inequality and complementarity theory as a tool,the optimal objective function of each participant is transformed into the corresponding variational inequality,and its economic significance is interpreted,and then the equilibrium model of the whole system is obtained.Then,using MATLAB software,the modified projection algorithm is used to deal with the variational inequality.Finally,in view of the model established in this paper,the third and fourth chapter,taking A automobile closed-loop supply chain system as an example to analyze,first built a simple three layers of closed-loop supply chain system,obtains its initial overall degree of brittleness,and the brittleness of the system was layered,through a series of processing on the improvement of the system is realized.Then,based on the system equilibrium model constructed by the fourth chapter,the corresponding real parameter and cost function are given,and the transaction volume between the participants is calculated by matlab software programming.The equilibrium solution of the system is obtained,and the sensitivity analysis of the system equilibrium solution under the probability of brittle risk is analyzed.The validity of the model constructed in this paper is verified.At the same time,it can provide theoretical guidance for the decision-making of closed-loop supply chain participants under brittle risk.