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

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

Mathematical and Computer Modelling of Dynamical Systems, 2010, vol. 16, issue 4, 373-388

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.

Date: 2010
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DOI: 10.1080/13873954.2010.511199

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