Multi-period supply chain network equilibrium with capacity constraints and purchasing strategies

In this paper, we propose a capacitated supply chain network equilibrium model in which three tiers of decision makers (manufacturers, retailers and consumers at demand markets) seek to determine their optimal plans over a multi-period planning horizon. Unlike other studies in the extent literature, we use a new concept of purchasing strategy to model the strategic behavior of retailers and consumers at demand markets in a capacitated supply chain network. A purchasing strategy denotes an ordered set of manufacturers (or retailers) from which each retailer (or each consumer at a demand market) prefers to purchase a product. We show that the equilibrium conditions governing the multi-period capacitated supply chain network equilibrium problem can be formulated as a variational inequality in terms of strategies and strategic flows. To find a solution to this variational inequality, we propose an iterative algorithm that generates strategies for retailers and consumers as required by solving a dynamic program. We prove that the solution set is nonempty and provide a numerical example to illustrate the validity of our model.