A Solution Algorithm for the Supply Chain Network Equilibrium Model

A supply chain network equilibrium problem was recently formulated using the variational inequality approach and solved with the modified projection method. Assuming the vector function F that enters the variational inequality is strictly monotone and Lipschitz continuous (and that a solution exists). The realization of the modified projection algorithm for the supply chain network equilibrium model is guaranteed to converge; however, its algorithmic steps are not so interesting to the transportation community as the concept of traffic assignment is not used. In this paper, a new solution algorithm that iteratively solves a fixed-demand traffic assignment problem and makes comparisons among intermediate solutions is proposed. The proposed algorithm is well explained by a supernetwork representation, and in addition, loosely justified by a numerical example. The proposed solution algorithm can be extended to solve the time-dependent/dynamic supply chain network equilibrium model without difficulty.