Abstract
In the classical economic order quantity (EOQ) models, a common unrealistic assumption is that all the items received are of good quality. However, in realistic environment, a received shipment usually contains a fraction of imperfect quality items. These imperfect items may be scrapped, reworked at a cost, or salvaged at a discounted price. While the percentage of imperfect items is random, the optimal ordering cycle is rarely considered in current literatures. This paper revisits the model (Maddah and Jaber, 2008) and extends it by assuming that the ordering cycle is determined by the demand rate, delivery quantity per shipment, and the mathematical expectation of the defective rate. The possibility of stockout or residue in the end of a cycle will be considered, and the loss of stockout and the salvage of the residue are counted into the cost. Besides, we consider consolidating the shipments of imperfect items over multiple deliveries. Thus, an integrated vendor-buyer inventory model for imperfect quality items with equal-size shipment policy is established to derive the optimal ordering cycle, ordering quantity, and number of deliveries. The computational method of the optimal delivery quantity per shipment and number of deliveries is given through theoretical results. Finally, sensitivity of main parameters is analyzed through simulation experiments and shown by some figures.
Highlights
Management’s view on inventory has been changed significantly over the several decades
Most of the researchers only presented the optimal order quantity when developing the models for imperfect items with random defective rate
When the cycle time is determined by the demand rate, delivery quantity per shipment, and the mathematical expectation of the defective rate, stockout and residue will happen in the end of a cycle due to the randomness of the defective rate, but there is no related discussion about the case of residue in current literatures
Summary
Management’s view on inventory has been changed significantly over the several decades. Hsu [27] developed different EPQ models with shortages backordered for cases of constant and random defective rate under three moments of withdrawing the defective items: (a) as they are detected, (b) at the end of each production period, or (c) at the end of each production cycle They derived out the optimal production lot size and backorder quantity and showed that the effects of both yield variability and withdrawal timing are not critical factors, which implicated that managements could make decisions by taking advantage of the mean defective rate when the probability density function of the defective rate is difficult to obtain. This study extends the model proposed by Maddah and Jaber [10] in three ways It considers the optimal ordering cycle by assuming that the cycle time is determined by the demand rate D, delivery quantity per shipment y, and the mathematical expectation of the defective rate p, just like that of Rezaei [6].
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