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Journal of Zhejiang University SCIENCE A 2010 Vol.11 No.12 P.938-945

http://doi.org/10.1631/jzus.A1001096


Dynamic robust optimal reorder point with uncertain lead time and changeable demand distribution


Author(s):  Masaki Tamura, Kazuko Morizawa, Hiroyuki Nagasawa

Affiliation(s):  Department of Electrical and Information Systems Engineering, Graduate School of Engineering, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan, Osaka Prefectural College of Technology, Neyagawa, Osaka 572-8572, Japan

Corresponding email(s):   tamuram08@eis.osakafu-u.ac.jp, morizawa@eis.osakafu-u.ac.jp, ngsw@ipc.osaka-pct.ac.jp

Key Words:  Reorder point, Lead time, Robust optimum, Uncertainty, Scenario


Masaki Tamura, Kazuko Morizawa, Hiroyuki Nagasawa. Dynamic robust optimal reorder point with uncertain lead time and changeable demand distribution[J]. Journal of Zhejiang University Science A, 2010, 11(12): 938-945.

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author="Masaki Tamura, Kazuko Morizawa, Hiroyuki Nagasawa",
journal="Journal of Zhejiang University Science A",
volume="11",
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pages="938-945",
year="2010",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1001096"
}

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%T Dynamic robust optimal reorder point with uncertain lead time and changeable demand distribution
%A Masaki Tamura
%A Kazuko Morizawa
%A Hiroyuki Nagasawa
%J Journal of Zhejiang University SCIENCE A
%V 11
%N 12
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%@ 1673-565X
%D 2010
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1001096

TY - JOUR
T1 - Dynamic robust optimal reorder point with uncertain lead time and changeable demand distribution
A1 - Masaki Tamura
A1 - Kazuko Morizawa
A1 - Hiroyuki Nagasawa
J0 - Journal of Zhejiang University Science A
VL - 11
IS - 12
SP - 938
EP - 945
%@ 1673-565X
Y1 - 2010
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A1001096


Abstract: 
In fixed order quantity systems, uncertainty in lead time is expressed as a set of scenarios with occurrence probabilities, and the mean and variance in demand distribution are supposed to be changeable according to a known pattern. A new concept of “dynamic robust optimal reorder point” is proposed in this paper and its value is calculated as a “robust optimal reorder point function with respect to reorder time”. Two approaches were employed in determining the dynamic optimal reorder point. The first is a shortage rate satisfaction approach and the second is a backorder cost minimization approach. The former aims at finding the minimum value of reorder point at each reorder time which satisfies the condition that the cumulative distribution function (CDF) of shortage rate under a given set of scenarios in lead time is greater than or equal to a basic CDF of shortage rate predetermined by a decision-maker. In the latter approach, the CDF of closeness of reorder point is defined at each reorder time to express how close to the optimal reorder points under the set of scenarios, and the dynamic optimal reorder point is defined according to stochastic ordering. Some numerical examples demonstrate the features of these dynamic robust optimal reorder points.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Leung, K.F., 2008. Using the complete squares method to analyze a lot size model when the quantity backordered and the quantity received are both uncertain. European Journal of Operational Research, 187(1):19-30.

[2]Mula, J., Poler, R., Garcia-Sabater, J.P., Lario, F.C., 2006. Models for production planning under uncertainty: a review. International Journal of Production Economics, 103(1):271-285. [doi:10.1016/j.ijpe.2005.09.001]

[3]Porteus, E.L., 1990. Stochastic Inventory Theory, Handbooks in Operations Research and Management Science. Heyman, D.P., Sobel, M.J. (Eds.), Stochastic Models, North-Holland, p.605-652.

[4]Tamura, M., Morizawa, K., Nagasawa, H., 2009. Robust Optimal Reorder Points with Uncertain Lead Time. Proceedings of the 10th Asia Pacific Industrial Engineering & Management System Conference, Kitakyuushu, Japan, p.1228-1239.

[5]Tersine, R.J., 1982. Principles of Inventory and Materials Management (2nd Ed.). North Holland, p.77-192.

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