This paper is concerned with the algorithm of the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model with elastic demands. Both models are further written as...This paper is concerned with the algorithm of the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model with elastic demands. Both models are further written as nonlinear complementarity problems. Semismooth least squares reformulations of the complementarity problems are presented and their convergence properties are investigated. Considering the drawbacks of Quasi-Newton method (using the Fischer-Burmeister function), a semi-smooth Levenberg-Marquardt-type method is proposed to solve the problems. Numerical examples show that the Levenberg-Marquardt-type method can solve the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model significantly, and is more efficient than the Quasi Newton method and the modified projection method. Furthermore, the Levenberg-Marquardt-type method with the equivalent supernetwork based complementarity formulation can be implemented faster than with the supply chain network equilibrium complementarity formulation.展开更多
基金supported by the National Basic Research Program of China("973" Program) (Grant No. 2006CB705503)the National Natural ScienceFoundation of China (Grant Nos. 70771005, 71071014, 70631001)the Fundamental Research Funds for Central Universities (Grant No.2009JBM044)
文摘This paper is concerned with the algorithm of the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model with elastic demands. Both models are further written as nonlinear complementarity problems. Semismooth least squares reformulations of the complementarity problems are presented and their convergence properties are investigated. Considering the drawbacks of Quasi-Newton method (using the Fischer-Burmeister function), a semi-smooth Levenberg-Marquardt-type method is proposed to solve the problems. Numerical examples show that the Levenberg-Marquardt-type method can solve the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model significantly, and is more efficient than the Quasi Newton method and the modified projection method. Furthermore, the Levenberg-Marquardt-type method with the equivalent supernetwork based complementarity formulation can be implemented faster than with the supply chain network equilibrium complementarity formulation.
