Research On Chern-simons-Schr(?)dinger System And Applications Of Dynamic Decision-making In Dual Channel Fresh Food Supply Chain

As fresh food has the characteristics of freshness,seasonality,attrition,perisha-bility,and consumers have higher and higher requirements for its quality,the coordi-nation of preservation and publicity and inventory control in the supply chain have become the difficulties of its management.Partial differential equation model is the basis of management mathematics research and provides a powerful tool for manage-ment.From the minimax method of differential games to deal with the robustness of many uncertain systems in management H_∞ problem provides a good idea for us to study the mathematical problems encountered in management.Minimax is a very useful method in nonlinear functional analysis to solve the existence of solutions of nonlinear partial differential equations in decision-making and optimization theory in management.Its main means is to transform the solution of the equation into finding the critical point of the energy functional corresponding to the equation.Therefore,finding the critical point of functional has become the key to solving the problem.This paper will study the behavior of the solution of the corresponding equation in the non degenerate case of the differential game model,and apply it to the dynamic decision-making problem of all kinds of dual channel fresh food supply chains.The main work of this paper is as follows:1.The green publicity differential game problem of dual channel fresh food supply chain considering the fresh-keeping investment level is studied.Firstly,the correspond-ing Hamilton-Jacobi-Bellman(HJB)equation in the case of centralized decision-making and Stackelberg decentralized decision-making is constructed.Secondly,a new Euler Lagrange energy functional is constructed by using the variable transformation method as the auxiliary equation,Combining the monotone method and minimax method to find the corresponding collinear Chern-Simons-Schr(?)dinger(CSS)minimum energy so-lution of the equation.Therefore,through the reverse induction method,the corre-sponding differential game equilibrium strategies of retailers and suppliers under the two kinds of decision-making situations are designed for the original problem,and then the contract is designed to make the supply chain system reach the state of coordi-nation mechanism,so that the expected profits of the members of the supply chain system are not lower than the corresponding profits under the Stackelberg game.Fi-nally,the effectiveness of the results is verified by simulation analysis with MATLAB software.2.The inventory control problem of dual channel fresh food supply chain consid-ering the fresh-keeping effort level,is studied,and the Hamilton-Jacobi-Bellman(HJB)equation is constructed in the no degenerate case where the maximum profit function of suppliers and retailers is satisfied in the case of differential game.Finding quasi-linear Chern-Simons-Schr(?)dinger(CSS)with the same solution characteristics through variable transformation and auxiliary combination of critical point theorem and Hardy-Littlewood-Sobolev inequality The minimum energy solution of the equation.Based on the improved basic deteriorating inventory model,this paper discusses the appli-cation of the characteristics of the solution to the optimal inventory differential game of two inventory modes of two-level dual channel supply chain considering the level of fresh-keeping effort and the decline of fresh food.3.The fresh-keeping cooperation strategy of fresh food supply chain with the inhibition of fresh-keeping effort level is studied,Using the constraint minimization and analysis techniques of Poho(?)aev-Nehari type,the co solution quasilinear Chern-Simons-Schr(?)dinger(CSS)of Hamilton-Jacobi-Bellman(HJB)equation in non degener-ate case is obtained The minimum energy solution of the equation.Then the maximum principle is applied to the corresponding differential decision model under the decen-tralized decision-making and centralized decision-making of the original problem.The optimal fresh-keeping effort level of suppliers and retailers and the optimal reputation of fresh food are obtained by reverse induction.Then,by comparing the strategies in the two decision-making situations,the contract with bilateral participation is de-signed to ensure the reasonable distribution of profits among supply chain members.Finally,through the simulation analysis of MATLAB software,the correctness of the results is verified.4.The preservation cooperation strategy of dual channel fresh food supply chain with the inhibition of preservation effort level is studied.Firstly,the behavior of the solution of the Chern-Simons-Schr(?)dinger(CSS)equation with the same solution of the Hamilton-Jacobi-Bellman(HJB)formula under the influence of multiple parameters is obtained through truncation technique and Brezis-Lieb.Secondly,based on the Nerlove-Arrow model,the existence of its solution is applied to the differential game model in which the preservation effort level has an inhibitory effect on the reputation of fresh food.The equilibrium strategy of retailers and suppliers under the two decisions is obtained by the reverse reduction method,and the optimal reputation of this kind of problem is obtained.By comparing the strategies under the two decision-making situations and adopting the bilateral subsidy strategy,the purpose of supply chain coordination can be achieved.