A multitiered framework for competitive flexible production value networks under environmental regulations

This paper introduces a novel framework for Flexible Production Value Networks (FPVNs) based on a variational inequality formulation that captures the decentralized behavior of suppliers, manufacturers, distributors, and demand markets under environmental and capacity constraints. The model establishes existence and uniqueness conditions for the equilibrium and is solved through a projection-type algorithm. Numerical illustrations on test networks demonstrate the effectiveness of the approach. In particular, the results show that the equilibrium solutions are stable with respect to demand and cost perturbations, and they highlight the role of environmental constraints in reshaping production and distribution strategies.