Dynamics of global supply chain supernetworks

In this paper, we develop a framework for the modelling, analysis, and computation of solutions to global supply chains. We consider three tiers of decision-makers: manufacturers, who may be located in the same or in different countries; intermediaries, in the form of retailers, who may be either physical or virtual, as in the case of electronic commerce; and consumers at the demand markets who may purchase the product in different currencies in the countries. We model the behavior of the decision-makers, derive the equilibrium conditions, and establish the variational inequality formulation. We then utilize the variational inequality formulation to obtain qualitative properties of the equilibrium product shipment and price pattern. In addition, we propose a dynamic adjustment process for the continuous time adjustment of the product flows and prices and formulate it as a projected dynamical system whose set of solutions coincides with the set of solutions to the variational inequality problem. A discrete-time algorithm is then applied to several numerical supply chain examples. This research extends the recent results surrounding the modelling of supply chains in a network equilibrium setting to the global arena.