In the context of demand shifting, a consideration is to be given to the (t, R) inventory decision making with multiple Markov demands. Priority is to be given to the consideration of the theory of multivariate Markov chains, with classical decision making methods and theories of (t, R) combined. A proposal has been made of a (t, R) inventory decision making model with multiple Markov demands, with an optimal (t, R) policy of the inventory system established, so as to determine the optimal order time and order quantity of the system. The basic conclusion of the model shows that the correlation between demands exerts an important influence on the optimal decision mechanism of the inventory system.