JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (9): 92-97.doi: 10.6040/j.issn.1671-9352.0.2017.023

Previous Articles     Next Articles

Optimal control polices for an inventory system with phase type distribution of lead time

ZHANG Shuang, YUE De-quan   

  1. School of Science, Yanshan University, Qinhuangdao 066004, Hebei, China
  • Received:2017-01-23 Online:2017-09-20 Published:2017-09-15

Abstract: A lost sales inventory system with phase type distribution of lead time and continuous-review (s, Q) replenishment policy was studied. Using the theory of Markov process, the steady state equilibrium equation was established, and the steady probability of the system was obtained. The minimum cost optimization model under certain service level was given. Using numerical example, the optimal inventory policy was calculated, and the sensitivity of the system parameters was analyzed.

Key words: inventory system, phase type distribution, (s, Q)policy, control policy

CLC Number: 

  • O226
[1] CHEN F Y, KRASS D. Inventory models with minimal service level constraints[J]. European Journal of Operational Research, 2001, 134(1):120-140.
[2] 唐应辉,唐小我. 排队论:基础与分析技术[M]. 北京:科学出版社,2006: 1-28. TANG Yinghui, TANG Xiaowo. Queuing theory: foundations and analytical techniques[M]. Beijing: Science Press, 2006: 1-28.
[3] 田乃硕,岳德权. 拟生灭过程与矩阵几何解[M]. 北京:科学出版社,2002: 1-38. TIAN Naishuo, YUE Dequan. Quasi-birth-and-death process and matrix geometric solution[M]. Beijing: Science Press, 2002: 1-38.
[4] 曾勇,董丽华,马建峰. 排队现象的建模、解析与模拟[M]. 西安:西安电子科技大学出版社,2011. ZENG Yong, DONG Lihua, MA Jianfeng. Modeling, analysis and simulation of queuing phenomenon[M]. Xian: Xidian University Press, 2011.
[5] BERMAN O, KIM E. Stochastic models for inventory management at service facilities[J]. Stochastic Models, 1999, 15(4):695-718.
[6] BERMAN O, SAPNA K P. Optimal control of service for facilities holding inventory[J]. Computers & Operations Research, 2001, 28(5):429-441.
[7] SAPNA K P. An (s, Q) Markovian inventory system with lost sales and two demand classes[J]. Mathematical and Computer Modelling, 2006, 43(7/8):687-694.
[8] BERMAN O, KIM E. Dynamic order replenishment policy in internet based supply chains[J]. Mathematical Methods of Operations Research, 2001, 53(3):371-390.
[9] 许一敏,张毕西,吴菊华. 对系统提前期/等待时间敏感的批量排队优化模型[J]. 工业工程与管理,2011,16(3):27-30. XU Yimin, ZHANG Bixi, WU Juhua. Sensitive to system lead time/waiting time batch queuing optimization model[J]. Industrial Engineering and Management, 2011, 16(3):27-30.
[10] 陈弘,刘名武,周宗放,等. 基于排队的库存服务系统最优控制策略[J]. 运筹与管理,2013,22(5):104-110. CHEN Hong, LIU Mingwu, ZHOU Zongfang, et al. Optimal control polices for an inventory service system based on the queueing theory[J]. Operations Research and Management Science, 2013, 22(5):104-110.
[1] CHEN Li, YANG Rui, MA Zhan-you. Performance analysis of Geom/G/1 queue with multiple vacations and set-up/close down period based on simulation experiment [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(08): 46-50.
[2] LIU Zai-ming, YU Sen-lin. A discrete time working vacations queuing system with different arrival rates and negative customers [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 1-6.
[3] FAN Jian-Wu, DIAO Xiao-Hua, TIAN Ai-Shuo, YUAN Xiao-Jing. The M/M/1/N queuing system with negative customers and a single working vacation [J]. J4, 2009, 44(8): 68-73.
[4] YUE Dequan, MA Jinwang, MA Mingjian, YU Jun. [J]. J4, 2009, 44(3): 39-44 .
[5] FU Yonghong 1, YU Miaomiao 2*, TANG Yinghui 3, LI Cailiang 4. [J]. J4, 2009, 44(4): 72-78 .
[6] ZHAO Xiao-hua,FAN Jian-wu,TIAN Nai-shuo,TIAN Rui-ling .

The M/M/1/N queuing system with balking, reneging and multiple working vacations

[J]. J4, 2008, 43(10): 46-51 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!