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Received: 2002-11-05

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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.1 P.117-122

http://doi.org/10.1631/jzus.2004.0117


A unified convergence theory of a numerical method,and applications to the replenishment policies


Author(s):  MI Xiang-jiang, WANG Xing-hua

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China

Corresponding email(s):   mxj0327@yahoo.com

Key Words:  Inventory, Shortages, Deterioration, Zero of derivative, Iteration, Optimization theory


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MI Xiang-jiang, WANG Xing-hua. A unified convergence theory of a numerical method,and applications to the replenishment policies[J]. Journal of Zhejiang University Science A, 2004, 5(1): 117-122.

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Abstract: 
In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But this approach requires calculation of the second derivative of the function. Avoiding this complex computation we use another iterative method presented by the second author. One of the goals of this paper is to present a unified convergence theory of this method. Then we give a numerical example to show the application of our theory.

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Reference

[1] Chu, P. and Chen, P.S., 2002. A note on inventory replenshment policies for deteriorating items in an exponentially declining market. Computers and Operations Research, 29:1827-1842.

[2] Ghare, P.M. and Schrader, G.F., 1963. A model for exponential decaying inventory. Journal of Industrial Engineering, 14(6):238-243.

[3] Wang, X.H., 1979. Convergent iteration method of order two for finding zeros of the derivative. Numer. Math. Sinica, 1(3):209-220.

[4] Wang, X.H., 1999. Convergence of Newton's method and inverse function in Banach spaces. Math. Comput., 68(3):169-186.

[5] Wang, X.H. and Li, C., 2001. On the convergent iteration method of order two for finding zeros of the derivative. MATHEMATICA NUMERICA SINICA, 23(1):121-128.

[6] Wang, X.H. and Li, C., 2003. On the united theory of the Family of Euler-Halley Type Methods with Cubical Convergence in Banach spaces. J.Comput.Math.,21(2):195-200.

[7] Yuan, Y.X. and Sun, W.Y., 1997. Optimization Theory and Methods. Science Press, Beijing.

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