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# An optimization model and method for supply chain equilibrium management problem

• * Corresponding authors: Guirong Pan and Bing Xue
• In this paper, we establish a nonlinear complementarity model and algorithm for supply chain equilibrium management problem consisting of manufacturers, retailers and consumer markets. This work focus on the price of the goods of retailer sell to consumer market in which is a function of the amount of products that are transacted between the retailer and the consumer. Based on this, we investigate the optimizing behavior of the various decision-makers, derive the equilibrium conditions of the manufacturers, the retailers and the consumer markets respectively, and establish a nonlinear complementarity model of this problem. To obtain optimal decision for the problem, we propose a new type of algorithm based on established model, and its global convergence is presented without the assumption of global Lipschitz continuous in detail. The efficiency of given algorithm is also illustrated through some numerical examples.

Mathematics Subject Classification: Primary: 90C30, 90C33; Secondary: 90B06.

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• Figure 1.  The network structure of the supply chain equilibrium problem

Figure 2.  The network structure of $i-$th manufacturer

Figure 3.  The network structure of $j-$th retailer

Figure 4.  The supply chain equilibrium management problem consists of 2 manufacturers, 1 retailer and 1 consumer market

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