有限耐烦期随机库存系统的最优控制

中国管理科学 ›› 2004, Vol. ›› Issue (2): 38-43.

有限耐烦期随机库存系统的最优控制

张小洪¹, 陈剑¹, 潘德惠²

1. 清华大学经济管理学院北京 100084;
2. 东北大学工商管理学院沈阳 110004

收稿日期:2003-09-02 修回日期:2004-03-10 出版日期:2004-04-28 发布日期:2012-03-07
基金资助:
国家自然科学基金资助项目(70231010、70329001);中国博士后基金资助项目(200303)

Optimal Control on Stochastic Inventory Systems with Time-Limited Free Backorders

ZHANG Xiao-hong¹, CHEN Jian¹, PAN De-hui²

1. School of Economics and Management, Tsinghua University, Beijing 100084, China;
2. School of Business Administration, Northeastern University, Shenyang 110004, China

Received:2003-09-02 Revised:2004-03-10 Online:2004-04-28 Published:2012-03-07

摘要/Abstract

摘要： 对供应链内部库存系统进行优化控制是提高供应链协调性的一种重要手段。本文针对实际库存活动中普遍存在的有限耐烦期这种现象,综合考虑顾客退货、库存损失等随机因素对最优库存策略的影响,构造出一种更加贴近实际的随机库存系统最优控制模型,并借助于动态规划原理给出了最优控制律的表达式,然后给出了算例及说明。其结果可为随机库存系统的管理决策提供了理论依据,也可为进一步提高供应链的协调性提供了借鉴。

关键词: 有限耐烦期, 随机库存系统, 最优控制, 供应链的协调

Abstract: Exercising optimal control on the internal stochastic inventory systems is essential to elevating the coordination of supply chain.We develop a practical model of optimal control on stochastic inventory system by considering the time-limited free backorders,which is usually a common phenomenon in the practical inventory activities,and the impact on optimal inventory law of stochastic factors,e.g.,return of sold goods,spoilage of stocked items,etc.And then,we obtain the optimal control law explicitly with the aid of dynamic programming.In addition,we give the numerical examples and illustrations.The results of this paper would provide theoretical evidence for making decisions on the inventory management and would make special reference further to elevating the coordination of supply chain.

Key words: time-limited free backorders, stochastic inventory systems, optimal control, coordination of supply chain

中图分类号:

F253.4

张小洪, 陈剑, 潘德惠. 有限耐烦期随机库存系统的最优控制[J]. 中国管理科学, 2004, (2): 38-43.

ZHANG Xiao-hong, CHEN Jian, PAN De-hui. Optimal Control on Stochastic Inventory Systems with Time-Limited Free Backorders[J]. Chinese Journal of Management Science, 2004, (2): 38-43.

参考文献

[1] 刘丽文,袁佳瑞.VMI环境下的库存与发货模型研究[J].中国管理科学,2003,11(5):31-36.
[2] Corbett C.J..Stochastic inventory systems in a supply chain with asymmetric information: cycle stocks, safety stocks and consignment stock [J]. Operations Research,2001,49(4):487-500.
[3] Cachon G P, Zipkin P.. Competitive and cooperative inventory policies in a two-stage supply chain[J]. Management Science, 1999,45 (7): 936-953
[4] 胡则成,罗荣桂,宋德昌,喻小军.随机存贮理论与应用[M].武汉:华中理工大学出版社,1994.
[5] Abbound N E, Sfairy R G. Time-limited free-back-orders EOQ model [J].Applied Mathematical Modelling,1997,21:21-25.
[6] 董云庭,王颖.一类两级DC/STORES库存系统模型与控制[J].中国管理科学,1998,6(1):40-47.
[7] Viswanathan, S. and R. Piplani, Coordinating supply chain inventories through common replenishment epoehs[J], European Journal of Operational Research, 129 (2): 277-286.
[8] Chiou, C., M. Yao and J.Tsai, Coordinating supply chain inventories through common replenishment epochs and quantity discounts[C]. International Conference on Global Supply Chain Management, Beijing, China, 2002:183-188.
[9] 黄会然,张小洪,潘德惠.线性需求且耐烦期有限的生产-库存模型[J].系统工程学报,2001,16(3):232-235.
[10] Sulem A. A solvable one-dimensional model of a diffusion inventory system [J].Mathematics of Operations Research, 1986,11 (1): 125-133.
[11] 张小洪,黄会然,潘德惠.一类单一物品随机库存系统的最优控制模型[J].系统工程学报,2002,17(1):56-61.
[12] Constantinides G, Richard S. Existence of optimal simple policies for discounted-cost inventory and cash management in continuous time [J]. Operations Research, 1978,26(4):620-636.
[13] 雍炯敏.动态规划方法与Hamilton-Jacobi-Bellman方程[M].上海:上海科学技术出版社,1992.
[14] Bellman R. Dynamic programming[M]. Princeton: Princeton University Press, 1957.
[15] 林元烈.应用随机过程[M].北京:清华大学出版社,2002.