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exec failed: Variational Inequality* _The equilibrium state governing the supply chain model according to the optimality conditions of the corresponding mathematical programmes is equivalent to the solution of the variational inequality problem given by: determine the equilibrium vectors of product shipments, shadow prices, and demand market prices %$(Q^{1*}, Q^{2*}, \gamma^*, \rho_{3}^*) \in \mathbb{R}_+^{mn+np+n+p}$% satisfying path