A supply chain network equilibrium model with a smoothing newton solution scheme

ABSTRACT

Considering that a supply chain comprises several independent decision makers, a supply chain network equilibrium model that consists of manufacturers, retailers and consumers is developed. After analysing the optimal conditions of various decision makers in the model, the equilibrium condition is established as an equivalent, finite-dimensional variational inequality formulation and is solved by a smoothing Newton method. The global and quadratic convergence of the method is established. The numerical results show the rapid convergence of the method. Additionally, the rapid convergence of the smoothing Newton method is beneficial when solving a complicated network model in the real world.