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Economic production quantity (EPQ) models under an imperfect production process with shortages backordered. (English) Zbl 1333.90035
Summary: In this paper, we develop economic production quantity (EPQ) models to determine the optimal production lot size and backorder quantity for a manufacturer under an imperfect production process. The imperfect production process is characterised by the fraction of defective items at the time of production $$\gamma$$. The paper considers different cases of the EPQ model depending on (1) whether $$\gamma$$ is known with certainty or is a random variable, and (2) whether imperfect items are drawn from inventory (a) as they are detected, (b) at the end of each production period or (c) at the end of each production cycle. Straightforward convexity results are shown and closed-form solutions are provided for the optimal order and backorder quantities for each of the cases we considered. We provide two numerical examples: one in which the defective probability follows a uniform distribution and the second which we assume follows a beta distribution, to illustrate the effects of yield variability and timing of the withdrawal of defectives on the optimal solutions. We obtain similar results for both numerical examples, which show that both the yield variability and the withdrawal timing are not critical factors.

##### MSC:
 90B30 Production models 90B05 Inventory, storage, reservoirs
##### Keywords:
EPQ; imperfect quality; inventory backorder
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##### References:
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