A Variational Inequality Framework for Multi-Echelon Supply Chains

This paper proposes a profit-maximization model for a multi-echelon supply chain, integrating transportation and inventory decisions within a unified framework. The system is formulated as a Variational Inequality, ensuring equilibrium conditions under convex costs and network constraints. By incorporating the Economic Order Quantity policy, inventory variables are eliminated, reducing model complexity. A projection method is used for computation, and numerical results illustrate the effectiveness of the approach in capturing realistic logistics behaviors.