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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。
Multiobjective stock newsboy model with multivariate Markov demand characteristics is considered. In this paper, the multivariate Markov process is used to describe the statistical regularity of the intrinsic motions of multi-product requirements. According to its motion characteristics, a multi-product Newsboy model with multivariate Markov needs is proposed. Under the framework of the new multi-product newsboy model, the optimal ordering strategy of multi-product inventory system is studied and the optimality of the model is analyzed by using the censoring probability, double-sided factor and the strength of the interdependence between requirements The nature of solution. The conclusion of the model shows that the optimal ordering strategy and the optimal profit expectancy are positively correlated with the truncation probability, and the relationship with the double-sided factor has a positive and negative correlation. Compared with the traditional multi-product newsboy model, the new model Has the unique superiority, fully considered the relationship between the demand of the strength of the optimal ordering strategy. At the same time, the feasibility and validity of the model theory are verified by numerical examples. The important management implications of this model in the inventory system optimization and control are also given.