Supply Chain Network Equilibrium Model Based On Generalized Nash Equilibrium

In the trend of economic globalization,outsourcing appear in front of people in a new form.Large-scale outsourcing is rapidly becoming the mainstream in the development of manufacturing industry.Especially after entering the twentieth Century,products outsourcing develop rapidly in all fields,the application of outsourcing theory to supply chain management has become a new business strategy,which enterprises through product outsourcing to reduce costs,and save resources.At the same time,with the introduction of the concept of outsourcing,the supply chain network structure becomes more complex,and the resource sharing becomes a common phenomenon.Due to the need of practical application,study the Nash Equilibrium problem began to slowly turned to the study of the Generalized Nash Equilibrium problem(GNEP).We develop a game theory model of supply chain network with product differentiation,outsourcing of production and distribution,and quality and price competition.The original firms compete with one another in terms of in-house quality levels and product flows,whereas the contractors aiming at maximizing their own profits,engage in competition for the outsourced production and distribution in terms of prices that they charge and their quality levels.We transform the generalized equilibrium problem into a variational inequality,which is then equivalent to the Mixed Complementarity Problem(MiCP),and then the complementarity problem is transformed into a nonlinear equation group by the F-B function.Because the research on nonlinear equations algorithm has been relatively mature,which can solve the problem fo the scale of supply chain,and slow speed solving of problems.In this paper,we use the smooth Newton-BiCG algorithm to solve the nonlinear equations which obtained the optimal quality level of the in-house manufactory,the optimal outsourcing quantity of the original firms and contractors product outsourcing optimal quality level as well as the optimal cost under the equilibrium state,which have certain realistic directive significance for the enterprises of supply chain to decided amount of outsourcing,the outsourcing price and scale of production.Finally,numerical examples are given to illustrate the effectiveness of the algorithm and the application of the model in practice.With the increasing voice of outsourcing,the gradual rise of the contractor,which makes the industry is in urgent need of efficient supply chain model and numerical methods.This paper made a comprehensive study on the generalized Nash Equilibrium problem of supply chain from the two aspects of the model and algorithm,with the use of economic value.