具有多元马氏需求的多产品多阶段库存优化模型

本文研究一类新的多产品库存控制策略,即具有多元马氏需求特征的多产品多阶段的订货点订货量(Q, R, SS)策略,该策略考虑市场需求在不同产品之间具有多元马氏转移特征,并考虑缺货因素设置安全库存。论文首先建立了多产品多阶段的多元马氏需求预测模型,并通过该模型确定了各种产品需求之间的关系。同时,在该模型的理论基础上,提出了多产品多阶段的总期望成本模型及其最优(Q, R, SS)策略,进而结合算例给出模型的最优策略的数值解。

Optimal Policy for Multi-product Multi-stage Inventory Model with Multivariate Markov Demand

The demands of muti-product would be correlated to each other in competitive market; therefore a better model for exploring these relationships and a better prediction rule for market's demand should be developed. Based on multivariate Markov theory, a new model is proposed to research these relationships and forecast the demand of muti-product. An expected total cost of muti-product model with high order multivariate Markov demand is constructed by the new model. Under these model conditions, a new type of multiple product inventory control policy is presented, which is multi-product and multi-stage inventory control (Q, R, SS) policy with multivariate Markov demand. This policy considers the optimal ordering quantity, optimal ordering point and safety stock setting in the multi-product and multi-stage inventory system. The conclusion shows that the optimality of (Q, R, SS) policy is correlation to the relationships of the demand among all kinds of products. Further, a numerical solution of optimal policy is provided to the model through a numerical example and it indicate that one can determine the optimal ordering quantity, optimal ordering point and safety stock from the new model by using the historical data of demand state.