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2013, 3(4): 655-664. doi: 10.3934/naco.2013.3.655

Dampening bullwhip effect of order-up-to inventory strategies via an optimal control method

Honglei Xu 1, , Peng Sui 2, , Guanglu Zhou 3, and  Louis Caccetta 3,

1. 

School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China
2. 

Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, China
3. 

Department of Mathematics and Statistics, Curtin University, Perth, WA, 6845, Australia, Australia

Received  March 2013 Revised  October 2013 Published  October 2013

In this paper, we consider the bullwhip effect problem of an Order-Up-To (OUT) inventory strategy for a supply chain system. We firstly establish a new discrete-time dynamical model which is suitable to describe the OUT inventory strategy. Then, we analyze the bullwhip effect for the dynamical model of the supply chain system. We thus transform the bullwhip effect's dampening problem to a discrete-time optimal control problem. By using the Pontryagin's maximum principle, we compute the corresponding optimal control and obtain the optimal manufacturer productivity of goods. Finally, we carry out numerical simulation experiments to show that the devised optimal control strategy is useful to dampen the bullwhip effect which always happens in the supply chain system.
Keywords: optimal control., order-up-to inventory strategy, Bullwhip effect.
Mathematics Subject Classification: Primary: 90B50; Secondary: 65P9.
Citation: Honglei Xu, Peng Sui, Guanglu Zhou, Louis Caccetta. Dampening bullwhip effect of order-up-to inventory strategies via an optimal control method. Numerical Algebra, Control & Optimization, 2013, 3 (4) : 655-664. doi: 10.3934/naco.2013.3.655
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show all references

References:
[1]

Irwin. 7th ed, 1995. Google Scholar

[2]

Management Science, 46 (2000), 436-443. Google Scholar

[3]

Int J Prod Res, 45 (2007), 351-368. Google Scholar

[4]

International Journal of Production Economics, 59 (1999), 251-259. Google Scholar

[5]

New York: MIT Press and John Wily &Sons, Inc, 1961.  Google Scholar

[6]

Management Science, 43 (1997), 546-558. Google Scholar

[7]

Stanford University Press, (1958), 109-134.  Google Scholar

[8]

John Wiley & Sons, New York, 1978. Google Scholar

[9]

European Journal Of Operational Research, 124 (2000), 495-510. Google Scholar

[10]

Ph.D. Dissertation, Department of Industrial Engineering and Management Science, Northwestern University, Evanston, 1997. Google Scholar

[11]

Martinus Nijhoff, Boston, 1981.  Google Scholar

[12]

Management Science, 35 (1989), 321-339. Google Scholar

[13]

Longman Scientific & Technical, New York, 1991.  Google Scholar

[14]

International Journal of Physical Distribution and Logistics Management, 22 (1992), 3-12. Google Scholar

[15]

Journal of Industrial and Management Optimization, 2 (2009), 81-94. doi: 10.3934/jimo.2009.5.81.  Google Scholar

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