Network model of inventory control in case of the price competition

The mathematical model of processes of cyclic transportation in logistic systems for a case of the price competition is investigated. We consider a network of a set stations, in each of which there are several enterprises with their warehouses. Enterprises supply and sell not exactly interchangeable products, the demand for which is deterministic. It is case of so called differential goods and customers can buy them at all prices. Each enterprise uses a relaxation method of inventory control with a deficiency assumption when modeling control systems. Existence conditions of the equilibrium decision for the model are given.