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Chinese Journal of Management Science ›› 2015, Vol. 23 ›› Issue (5): 151-160.doi: 10.16381/j.cnki.issn1003-207x.2015.05.019

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

CHEN Jie1,2, CHEN Zhi-xiang1   

  1. 1. School of Business, Sun Yat-sen University, Guangzhou 510275, China;
    2. School of Science and Engineering, Qiongzhou University, Sanya 572022, China
  • Received:2013-05-02 Revised:2014-02-04 Online:2015-05-20 Published:2015-05-20

Abstract: 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.

Key words: multi-product and multi-stage inventory, multivariate Markov model, optimal (Q, R, SS) policy

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