Numerical method for determination of the optimal lot size for a manufacturing system with discontinuous issuing policy and rework

Abstract

This paper employs numerical method for determination of the optimal lot size for a manufacturing system with discontinuous inventory issuing policy and imperfect rework of random defective items. The classic economic manufacturing quantity (EMQ) model assumes a continuous issuing policy for satisfying customer's demands, and perfect quality production for all items produced during a production run. However, in a real-life vendor–buyer integrated system, the discontinuous issuing policy such as multi-shipment policy is practically used in lieu of continuous issuing policy, and it is inevitable to generate defective items during a production run. Imperfect quality items fall into two groups: the scrap and the reworkable. During the rework process, failure in repair exists; a portion of reworked items fails and becomes scrap. The finished items can only be delivered to customers if the whole lot is quality assured at the end of the rework. Mathematical modeling and analysis are used to deal with the proposed model, and the long-run average cost function is derived. Convexity of this cost function is proved and a closed-form optimal batch size solution to the problem is obtained. Two special cases are examined and a numerical example demonstrates its practical usage. Copyright © 2010 John Wiley & Sons, Ltd.

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