具有多元马氏需求的多产品多阶段库存优化模型

doi:10.16381/j.cnki.issn1003-207x.2015.05.019

中国管理科学 ›› 2015, Vol. 23 ›› Issue (5): 151-160.doi: 10.16381/j.cnki.issn1003-207x.2015.05.019

具有多元马氏需求的多产品多阶段库存优化模型

陈杰^1,2, 陈志祥¹

1. 中山大学管理学院, 广东广州 510275;
2. 琼州学院理工学院, 海南三亚 572022

收稿日期:2013-05-02 修回日期:2014-02-04 出版日期:2015-05-20 发布日期:2015-05-20
作者简介:陈杰(1979-),男(汉族),海南临高人,琼州学院理工学院副教授,中山大学管理学院博士研究生,研究方向:马氏决策优化、管理系统仿真与优化.
基金资助:
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);海南省高等学校科学研究基金项目(HJKJ2012-42)

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

CHEN Jie^1,2, CHEN Zhi-xiang¹

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

摘要/Abstract

摘要： 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。

关键词: 多产品多阶段库存, 多元马尔可夫模型, 最优(Q, R, SS)策略

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

中图分类号:

陈杰, 陈志祥. 具有多元马氏需求的多产品多阶段库存优化模型[J]. 中国管理科学, 2015, 23(5): 151-160.

CHEN Jie, CHEN Zhi-xiang. Optimal Policy for Multi-product Multi-stage Inventory Model with Multivariate Markov Demand[J]. Chinese Journal of Management Science, 2015, 23(5): 151-160.

参考文献

[1] Dvoretzky A, Kiefer J, Wolfowitz J. The inventory problem:Case of known distributions of demand[J]. Econometrica: Journal of the Econometric Society, 1952, 20(2):187-222.

[2] Shao Zhen, Ji Xiaoyu. Fuzzy multi-product constraint newsboy problem[J]. Applied Mathematics and Computation, 2006, 180(1): 7-15.

[3] Haksever C, Moussourakis J. Determining order quantities in multi-product inventory systems subject to multiple constraints and incremental discounts[J]. European Journal of Operational Research, 2008, 184(3): 930-945.

[4] Taleizadeh A A, Niaki S T A, Aryanezhad M B. A hybrid method of Pareto, TOPSIS and genetic algorithm to optimize multi-product multi-constraint inventory control systems with random fuzzy replenishments[J]. Mathematical and Computer Modelling, 2009,49(5): 1044-1057.

[5] Cárdenas-Barrón L E, Treviño G, Wee H M. A simple and better algorithm to solve the vendor managed inventory control system of multi-product multi-constraint economic order quantity model[J]. Expert Systems with Applications, 2012, 39(3): 3888-3895.

[6] Yang Xu, Heragu S S, Evans G W. Integrated production-inventory-distribution optimization in a multi-echelon, multi-product, multi-carrier, multi-period system[J]. International Journal of Value Chain Management, 2010, 4(3): 267-287.

[7] Choi S, Ruszczyński A. A multi-product risk-averse newsvendor with exponential utility function[J]. European Journal of Operational Research, 2011, 214(1): 78-84.

[8] Murray C C, Gosavi A, Talukdar D. The multi-product price-setting newsvendor with resource capacity constraints[J]. International Journal of Production Economics, 2012, 138(1): 148-158.

[9] De Schrijver S K, Aghezzaf E H, Vanmaele H. Aggregate constrained inventory systems with independent multi-product demand: Control practices and theoretical limitations[J]. International Journal of Production Economics, 2013,143(2):416-423.

[10] Zhou Weiqi, Chen Long, Ge Huiming. A multi-product multi-echelon inventory control model with joint replenishment strategy[J]. Applied Mathematical Modelling, 2013, 37(4): 2039-2050.

[11] 秦进,史峰,缪立新,等.考虑随机需求和库存决策的多商品物流网络设计优化模型与算法[J]. 系统工程理论与实践,2009,29(4):176-183.

[12] 胡玉梅,胡劲松,杨飞雪,等.模糊随机需求下多产品报童问题的均衡策略[J]. 运筹与管理,2011,20(1):72-77.

[13] 黄松,杨超,张曦.考虑战略顾客行为带预算约束的多产品报童问题[J]. 中国管理科学, 2011, 19(3): 70-78.

[14] 周欣,霍佳震.循环取货下基于随机提前期波动压缩的库存优化模型[J]. 系统工程理论与实践,2012,32(4):760-768.

[15] 李季,周李超,王汉生.多产品协同促销模式下的零售商促销时间决策模型[J]. 中国管理科学,2013,21(4):89-97.

[16] Karlin S. Dynamic inventory policy with varying stochastic demands [J]. Management Science, 1960, 6(3): 231-258.

[17] Song Jingsheng, Zipkin P. Inventory control in a fluctuating demand environment[J]. Operations Research, 1993, 41(2): 351-370.

[18] Chen Fangruo, Song Jingsheng. Optimal policies for multiechelon inventory problems with Markov-modulated demand[J]. Operations Research, 2001, 49(2): 226-234.

[19] Raftery A E. A model for high-order Markov chains[J]. Journal of the Royal Statistical Society. Series B (Methodological), 1985,47(3): 528-539.

[20] Ching W K, Fung E S, Ng M K. A multivariate Markov chain model for categorical data sequences and its applications in demand predictions[J]. IMA Journal of Management Mathematics, 2002, 13(3): 187-199.

[21] Ching W K, Ng M K, Fung E S. Higher-order multivariate Markov chains and their applications[J]. Linear Algebra and its Applications, 2008, 428(2): 492-507.

[22] 楼润平,薛声家.两个实用的安全库存公式[J]. 系统工程,2008,26(12):77-82.

具有多元马氏需求的多产品多阶段库存优化模型

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

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