Abstract: In practice, many companies have more than one product in inventory, and multi-product inventory control problem is more complicated than single product inventory control problem. At present, the multi-product inventory problem has aroused widespread attention, However, most authors only consider independently demands, little attention has been paid to the inventory with dependent demands. In fact, some multiple data sequences of the demands are correlated to each other, and these correlations impact on the optimal policy for multiple products inventory system. To explore the relationships among the demands and characterize the statistical law of inner movement for the demands of multiple products, these multiple data sequences are modelled by using multivariate Markov processes, and the multi-product newsvendor model with multivariate Markovian demand is proposed according to the movement characteristics of the demands. Under the theoretical framework of the new multi-product newsvendor model, the optimal ordering policy for the multi-product inventory system is studied, and the properties of the solution for model are analyzed through the truncated probability, dual factors and strength of relationships among the demands. The conclusion demonstrates that the optimality of ordering policy has a positive correlation with expected profit related to the truncated probability and a paradoxical relation with the dual factors; there is a unique advantage on the new model compare with the conventional multi-product newsvendor model, that is the strength of the demand correlation impact on the optimal ordering policy is fully considered. Moreover, the feasibleness and effectiveness for the model are verified through the numerical example, and some important management implications of the model are given for the optimization and control in the inventory system. From the new model, the relationships among competitive products are modeled, and decision-maker can obtain the information for the correlations of demands impact on the optimal ordering policy.

Key words: multivariate Markovian demand, multi-product newsvendor model, truncated probability, dual factors, optimality of ordering policy