Inventory Models with Defective Units and Sub-Lot Inspection

Han-Wen Tuan, Gino K. Yang and Kuo-Chen Hung
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Han-Wen Tuan: Department of Computer Science and Information Management, Hungkuang University, Taichung 43302, Taiwan
Gino K. Yang: Department of Computer Science and Information Management, Hungkuang University, Taichung 43302, Taiwan
Kuo-Chen Hung: Department of Computer Science and Information Management, Hungkuang University, Taichung 43302, Taiwan

Mathematics, 2020, vol. 8, issue 6, 1-13

Abstract: Inventory models must consider the probability of sub-optimal manufacturing and careless shipping to prevent the delivery of defective products to retailers. Retailers seeking to preserve a reputation of quality must also perform inspections of all items prior to sale. Inventory models that include sub-lot sampling inspections provide reasonable conditions by which to establish a lower bound and a pair of upper bounds in terms of order quantity. This should make it possible to determine the conditions of an optimal solution, which includes a unique interior solution to the problem of an order quantity satisfying the first partial derivative. The approach proposed in this paper can be used to solve the boundary. These study findings provide the analytical foundation for an inventory model that accounts for defective items and sub-lot sampling inspections. The numerical examples presented in a previous paper are used to demonstrate the derivation of an optimal solution. A counter-example is constructed to illustrate how existing iterative methods do not necessarily converge to the optimal solution.

Keywords: distribution-free inventory model; defective items; sub-lot sampling inspection; backordered rate; crashable lead time (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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