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Some improved algorithms to locate the optimal solutions for exponentially deteriorating items under trade credit financing in a supply chain system. (English) Zbl 1221.90012

Summary: The Taylor series approximations neglecting the third and higher order terms in the expansion of \(e^{x}\) are frequently used by many researchers to get closed-form solutions to simplify the solution procedure to locate the optimal solution. However, they may cause significant penalty costs sometimes. Under some assumptions, K.N. Huang and J.J. Liao [Comput. Math. Appl. 56, No. 4, 965–977 (2008; Zbl 1155.90310)] showed that the total relevant cost per year is convex. With the convexity, they develop the solution procedures to locate the optimal cycle times to avoid the shortcoming of the significant penalty cost that the Taylor series approximations may cause. The main purpose of this paper not only removes those assumptions about the convexities of the total relevant costs per year described in [loc. cit.] but also presents some simplified solution procedures free of using the convexity to improve [loc. cit.].

MSC:

90B05 Inventory, storage, reservoirs

Citations:

Zbl 1155.90310
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References:

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[2] Chung, K. J.; Hou, K. L.; Lan, S. P., The optimal production cycle time in an integrated production—inventory model for decaying raw materials, Applied Mathematical Modelling, 33, 1-10 (2009) · Zbl 1167.90318
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[4] Huang, K. N.; Liao, J. J., A simple method to locate the optimal solution for exponentially deteriorating items under trade credit financing, Computers and Mathematics with Applications, 56, 965-977 (2008) · Zbl 1155.90310
[5] Varberg, D.; Purcell, E. J.; Steven, S. E., Calculus (2007), Pearson Education, Inc.: Pearson Education, Inc. Upper Saddle River, NJ, pp. 87-88, 07458
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