An efficient algorithm for solving supply chain network equilibria and equivalent supernetwork based traffic network equilibria

Abstract

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.supply chain networks, traffic network equilibrium, supernetwork, nonlinear complementarity problem, LevenbergMarquardt-type method Citation:Xu M, Gao Z Y. An efficient algorithm for solving supply chain network equilibria and equivalent supernetwork based traffic network equilibria. Sci

Research on Bus and Metro Transfer From Perspective of Hypernetwork—A Case Study of Xi’an, China (December 2020)

“…Xu et al (2008) [3] studied the equivalent traffic network equilibrium model of supply chain network equilibrium model with elastic demand, expressed it as a nonlinear complementarity problem, and solved it by Levenberg Marquardt type method. Then, Xu et al (2010) [4] studied the supply chain network equilibrium model based on elastic demand and the equivalent transportation network equilibrium model based on hypernetwork, proposed a new semi-smooth Levenberg Marquardt algorithm, and proved that it is more effective than Newton method and modified projection method; Feng et al (2014) [5] established a hypernetwork model of the closed-loop supply chain in demand market, including suppliers, manufacturers, retailers and consumers. The equilibrium conditions of the closed-loop supply chain were solved by using evolutionary variational inequality theory and dynamic prediction system, and numerical examples verified the rationality of the model; [6] established a hypernetwork model of reverse logistics supply chain with six decision makers, described the seasonal influence of demand on simple periodic function, and described the equilibrium state of the network by using the theory of variational inequality.…”

Analysis of the projective synchronization of the urban public transportation super network

“…In the field of transportation, the super-network research mainly focused on the optimization study of the equilibrium model of transportation supply chain network; Xu and Gao 16 proposed a new and efficient algorithm for solving supply chain network equilibrium and equivalent super network-based traffic network equilibrium. The new method was called semi-smooth LevenbergMarquardt-type method which was verified more efficient than the Quasi Newton method and the modified projection method to solve the problem.…”

“…In recent years, with the emergence of super-network research, the application of super network in all fields has been given much attention, such as electricity network, 12 social network, 13,14 the knowledge structure network, 15 and supply chain network. In the field of transportation, the super-network research mainly focused on the optimization study of the equilibrium model of transportation supply chain network; Xu and Gao 16 proposed a new and efficient algorithm for solving supply chain network equilibrium and equivalent super network-based traffic network equilibrium. The new method was called semi-smooth Levenberg-Marquardt-type method which was verified more efficient than the Quasi Newton method and the modified projection method to solve the problem.…”