Optimization of Multi-Tiered Supply Chain Networks with Equilibrium Flows

Consider a multi-tiered supply chain network which contains manufacturers, distributors and consumers. A manufacturer located at the top tier of this supply chain is supposed to be concerned with the production of products and shipments to the distributors for profit maximization. In turn, a distributor located in the middle tier of the supply chain is faced with handling and managing the products obtained from manufacturers as well as conducting transactions with consumers at demand markets. The consumer, who is the ultimate user for the product in the supply chain, located at the bottom tier of the supply chain agrees to the prices charged by distributors for the product if the associated business deal is done. The underlying behaviour of manufacturers, distributors and consumers is supposed to compete in a non-cooperative manner. Each decision maker individually wishes to find optimal shipments given the ones of other competitors. The problem of deciding optimal shipments in a supply chain equilibrium network was firstly noted by Nagurney et al. (2002). Dong et al. (2004) developed a supply chain network model where a finite-dimensional variational inequality was formulated for the behaviour of various decision makers. Zhang (2006), in turn, proposed a supply chain model that comprises heterogeneous supply chains involving multiple products and competing for multiple markets. In this chapter we develop an optimal solution scheme for a multi-tiered supply chain network which contains manufacturers, distributors and consumers. In the multi-tiered supply chain network, there are two kinds of decision-making levels investigated: the management level and the operations level. For the management level, the decision maker wishes to find a set of optimal policies which aim to minimize total cost incurred by the whole supply chain network. For the operations level, assuming the underlying behaviour of the multi-tiered decision makers compete in a non-cooperative manner, each decision maker individually wishes to find optimal shipments given the ones of other competitors. Therefore a problem of deciding equilibrium productions and shipments in a multi-tiered supply chain network can be established. Nagurney et al. (2002) were the first ones to recognize the supply chain equilibrium behaviour, in this chapter, we enhance the modelling of supply chain equilibrium network by taking account of policy interventions at