Abstract: Under the free competitive market, one of the basic attributes of modern commodities is competitive relationships among the multiple products. It means multi-product inventory control system has to be built on information of demands with competition. Newsvendor model is one of the most important and basic theoretical approach of making optimal ordering policy for the multi-product inventory system. Therefore, a multi-product newsvendor problem is discussed under the situation with competition in this article. First, in order to characterize the competitive relationships among the multiple products, a demand transition model is constructed by using the Markov chain. And then, two core concepts as Markov competitive factors and comprehensive competitive power are proposed in accordance with the transition probability matrix in the model. Furthermore, the competitive factors are incorporated into the framework of classic newsvendor model and combining convolution formula and Jacobian determinant to the multi-product newsvendor model with competitive factors, and the new decision-making mechanism is derived from the model. Finally, the numerical examples are given to analysis in the condition of competitive relationship between the 3 products. The numerical examples show that the competitive factors have an important impact on the optimal ordering polices in the inventory system in which the optimality of ordering quantity is increasing in the comprehensive competitive power, and the data experiment results also demonstrate that the adaptability of the newsvendor model in the practical application and the effectiveness of optimization and control in the inventory system would be further improved when the competitive factors were incorporated into the decision-making mechanism.

Key words: Markov chain, competitive factors, comprehensive competitive power, multi-product newsvendor model