考虑具有多元马氏需求特征的多产品库存报童模型的优化问题。本文利用多元马尔可夫过程描述多产品需求的内在运动的统计规律性，并根据其运动特征提出带有多元马氏需求的多产品报童模型。在新的多产品报童模型的理论框架下，研究了多产品库存系统的最优订购策略，并利用需求状态的截尾概率、双面因子及需求间关联性的强弱分析了该模型最优解的性质。模型的结论表明：最优订购策略和最优期望利润与截尾概率的关系为正相关，与双面因子的关系则具有正反的关联性；较于以往的多产品报童模型，新的模型具有独特的优越性，即充分考虑了需求间关联性的强弱对最优订购策略的影响。同时，通过数值算例验证了模型理论的可行性和有效性，并给出该模型在库存系统优化与控制中的重要管理启示。
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.
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