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Mathematical modelling for determining economic batch size and optimal number of deliveries for EPQ model with quality assurance

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  • Yuan-Shyi Peter Chiu
  • Chih-An Katherine Lin
  • Huei-Hsin Chang
  • Victoria Chiu

Abstract

The classic economic production quantity (EPQ) model assumes a continuous inventory-issuing policy for satisfying product demand and a perfect production for all items produced. However, in a real-life vendor--buyer integrated system, a multi-delivery policy is often used in lieu of continuous issuing policy and it is inevitable to generate defective items during a production run. This study addresses these issues by incorporating multiple deliveries of the finished batch, customer's inventory-holding cost and manufacturer's quality assurance cost into an EPQ model with the imperfect reworking of random defective items. Mathematical modelling and analyses are employed. Convexity of the long-run expected cost function is proved by the use of Hessian matrix equations, and the closed-form solutions in terms of the optimal lot size and optimal number of deliveries are obtained. The research results are demonstrated with a numerical example with a discussion on its practical usage.

Suggested Citation

  • Yuan-Shyi Peter Chiu & Chih-An Katherine Lin & Huei-Hsin Chang & Victoria Chiu, 2010. "Mathematical modelling for determining economic batch size and optimal number of deliveries for EPQ model with quality assurance," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 16(4), pages 373-388, July.
    • Handle: RePEc:taf:nmcmxx:v:16:y:2010:i:4:p:373-388
    DOI: 10.1080/13873954.2010.511199
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    References listed on IDEAS

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    1. Gerardo Treviño-Garza & Krystel K. Castillo-Villar & Leopoldo Eduardo Cárdenas-Barrón, 2015. "Joint determination of the lot size and number of shipments for a family of integrated vendor–buyer systems considering defective products," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(9), pages 1705-1716, July.
    2. Amir Hossein Nobil & Amir Hosein Afshar Sedigh & Leopoldo Eduardo Cárdenas-Barrón, 2020. "A multiproduct single machine economic production quantity (EPQ) inventory model with discrete delivery order, joint production policy and budget constraints," Annals of Operations Research, Springer, vol. 286(1), pages 265-301, March.
    3. Chiu, Singa Wang & Wu, Cheng-Sian & Tseng, Chao-Tang, 2019. "Incorporating an expedited rate, rework, and a multi-shipment policy into a multi-item stock refilling system," Operations Research Perspectives, Elsevier, vol. 6(C).

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