A network inventory control model in the case of quantitative competition

Under study is a mathematical model of processes of cyclic transportation in logistic systems for the case of quantitative competition. We consider a network of a set of stations at each of which there are several enterprises with their warehouses. Enterprises supply and sell homogeneous products the demand for which is deterministic. Each enterprise uses a relaxation method of inventory control with the assumption of deficiency when modeling control systems. Existence conditions for an equilibrium solution for the model are given.