The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models

Ting-Chen Hu, Kuo-Chen Hung and Kuo-Lung Yang
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Ting-Chen Hu: Department of Health Business Administration, Hungkuang University, Taichung City 43302, Taiwan
Kuo-Chen Hung: Department of Computer Science and Information Management, Hungkuang University, Taichung City 43302, Taiwan
Kuo-Lung Yang: Department of Computer Science and Information Management, Hungkuang University, Taichung City 43302, Taiwan

Mathematics, 2019, vol. 7, issue 5, 1-10

Abstract: For inventory models with unknown distribution demand, during shortages, researchers used the first and the second moments to derive an upper bound for the worst case, that is the min-max distribution-free procedure for inventory models. They applied an iterative method to generate a sequence to obtain the optimal order quantity. A researcher developed a three-sequence proof for the convergence of the order quantity sequence. We directly provide proof for the original order quantity sequence. Under our proof, we can construct an increasing sequence and a decreasing sequence that both converge to the optimal order quantity such that we can obtain the optimal solution within the predesigned threshold value.

Keywords: inventory models; minimax distribution-free procedure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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