Chung, Kun-Jen 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 Comput. Math. Appl. 61, No. 9, 2353-2361 (2011). 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.]. Cited in 2 Documents MSC: 90B05 Inventory, storage, reservoirs Keywords:inventory; cash discount; delay payments; deteriorating items; trade credit Citations:Zbl 1155.90310 PDFBibTeX XMLCite \textit{K.-J. Chung}, Comput. Math. Appl. 61, No. 9, 2353--2361 (2011; Zbl 1221.90012) Full Text: DOI References: [1] Park, K. S., An integrated production—inventory model for decaying raw materials, International Journal of Systems Science, 14, 801-806 (1983) [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 [3] Chang, C. T.; Teng, J. T., Retailer’s optimal ordering policy under supplier credits, Mathematical Methods of Operations Research, 60, 471-483 (2004) · Zbl 1104.90007 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.