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Inventory Models with Defective Units and Sub-Lot Inspection

Author

Listed:
  • 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)

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.

Suggested Citation

  • Han-Wen Tuan & Gino K. Yang & Kuo-Chen Hung, 2020. "Inventory Models with Defective Units and Sub-Lot Inspection," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1038-:d:376315
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    References listed on IDEAS

    as
    1. Chang Wook Kang & Misbah Ullah & Biswajit Sarkar & Iftikhar Hussain & Rehman Akhtar, 2017. "Impact of random defective rate on lot size focusing work-in-process inventory in manufacturing system," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1748-1766, March.
    2. Naoufel Cheikhrouhou & Biswajit Sarkar & Baishakhi Ganguly & Asif Iqbal Malik & Rafael Batista & Young Hae Lee, 2018. "Optimization of sample size and order size in an inventory model with quality inspection and return of defective items," Annals of Operations Research, Springer, vol. 271(2), pages 445-467, December.
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