A time-dependent supply chain network equilibrium problem

This chapter deals with a time-dependent supply chain network equilibrium (TD-SCNE) problem, which allows product flows to be distributed over a network, not only between two successive sectors in the same time period (a transaction), but also between two successive periods for the same agency (an inventory). Since product price and flow interactions are inherently embedded within it, the TD-SCNE problem is formulated as a variational inequality (VI) model. A three-loop-nested diagonalization method, along with a specially designed supernetwork representation, then is proposed and demonstrated with a numerical example. In equilibrium, for each time-dependent retailer agency or demand market, the product prices of transactions are the same and minimum, no matter when or where the product comes from, which is a realization of the Wardropian first principle. The proposed framework can be extended with minor modifications to other TD-SCNE-related equilibrium problems.