Supply chain network equilibrium with asymmetric variable demand and cost functions

The supply chain network equilibrium (SCNE) problem is to study the effect of interactions of several economic sectors in a supply chain. The corresponding equilibrium conditions can be characterized by the Wardrop second principle. Due to link interactions, possibly asymmetric, embedded in the variable demand and cost functions, the SCNE problem was traditionally formulated as a variational inequality (VI) model and solved by the modified projection method. This paper proposes an alternative solution algorithm, named the nested diagonalization solution algorithm, for solving the SCNE problem by transforming it into a series of variable demand traffic assignment problem for which the Frank-Wolfe algorithm can easily be applied. The proposed algorithm, which can better be illustrated by its associated supernetwork representation, is validated with the same numerical example of Nagurney et al. (2002).