带有能力约束的多元马氏需求报童模型  

Capacitated newsboy model with multivariate Markovian demand

作　　者：陈杰[1,2] 陈志祥[1] 邢灵博 陈崇萍[1] 

机构地区：[1]中山大学管理学院,广州510275 [2]海南热带海洋学院数学系,三亚572022

出　　处：《管理科学学报》2016年第7期37-49,共13页Journal of Management Sciences in China

基　　金：国家自然科学基金资助项目(71372154);海南省自然科学基金资助项目(20151008);教育部人文社会科学研究青年基金资助项目(15YJC630013)

摘　　要：在随机需求环境下考虑带有能力约束的多产品报童问题.为了对多产品的需求进行预测,并度量其需求间的关系,本文首先建立了多元马氏需求模型.其次,在该模型的理论基础上,提出了带有能力约束的多元马氏需求报童模型,进而给出多产品的最优订购策略解.最后,利用期望需求状态的概率值及其截尾概率分析了模型最优解的性质.模型的结论表明,在能力约束的条件下,最优订购量关于左截尾概率单调递减,关于右截尾概率单调递增,而期望需求状态的概率值对最优订购量具有双重的特殊影响.In this paper, a muhi-product capacitated newsvendor model with stochastic demand is studied. Firstly, a multivariate Markovian demand model to forecast the demands of multiple products is constructed, and the relationships among the demands are measured by the model. Secondly, a capacitated newsboy model with multivariate Markovian demand is proposed, and then the solution of optimal ordering policy for multiple products is derived. At last, the properties of the optimal policy through the probability value and truncated probability of the expected demand state are discussed. With capacity constrains, the theoretical analysis shows that the optimal ordering quantity is a monotonic decreasing function with respect to the left truncated probability, and a monotonic increasing function with respect to the right truncated probability, but the probability value of the expected demand state has special dual effects on the optimal ordering quantity.

关 键 词：多元马氏链 多产品报童模型 能力约束 截尾概率 最优订购策略 

分 类 号：O211.62[理学—概率论与数理统计] F253.4[理学—数学]