带有马尔可夫竞争因子的多产品报童模型

在竞争的环境下考虑多产品报童问题。为了刻画多产品间的竞争关系,本文利用马尔可夫链构建多产品的需求转移模型,并根据模型的转移概率矩阵提出马氏竞争因子和综合竞争力等核心概念,进而结合卷积公式和雅可比行列式,将竞争因子的概念纳入经典报童模型的框架,构建了带有马氏竞争因子的多产品报童模型,同时在该模型的理论基础上给出了新的决策机制。模型的数据实验表明:竞争因子对多产品库存系统的最优订购策略具有重要的影响,关于产品的综合竞争力为单调递增函数;将竞争因子纳入多产品库存系统的决策机制,可进一步拓展报童模型在实际应用领域中的适应性以及提高库存系统的优化与控制的效用。

Multi-product Newsvendor Model with Markov Competitive Factors

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.