Hsu and Hsu (2013a) established a closed-form solution for an EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns, where the customers who return the defective items will receive full price refunds; i.e., the returned items are not replaced with good items. In this note, we extend Hsu and Hsu & apos; s (2013a) work to consider the case that returned items are replaced with good items. A closed-form solution is developed for the optimal order size and the maximum shortage level. Numerical examples are provided to show the differences in the optimal solutions when returned items are replaced, and when they are not.

In this paper, we develop an integrated vendor-buyer production-inventory model for items with imperfect quality and inspection errors. The production process is imperfect and produces a certain number of defective items with a known probability density function. We consider the policy in which the delivery quantity to the buyer is identical at each shipment. Once the buyer receives the lot, a 100% screening process of the lot is conducted, and the screening process and demand proceed simultaneously. The screening process is not perfect. The inspector may incorrectly classify a non-defective item as defective, or incorrectly classify a defective item as non-defective. The expected integrated total annual cost of the vendor and the buyer is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer.

Wee et al. (2007) developed an optimal inventory model. In this technical note, we point out a contradiction between Wee et al. & apos; s model and their assumption. A corrected model is developed based on their assumption. Numerical examples show that in terms of the two decision variables, there is a significant difference between the corrected model and Wee et al. & apos; s model. The results also show that that the penalty of using Wee et al. & apos; s model can be significant under certain situations.

In a previously published paper by Khan et al. (2011) [Khan, M., Jaber, M.Y., & Bonney M. (2011). An economic order quantity (EOQ) for items with imperfect quality and inspection errors, International Journal of Production Economics, 133, 113-118], we found that there is a contradiction between the cycle length and the holding cost per cycle. To obtain the cycle length, the authors assumed that the returned items from the market were replaced with good quality items. However, for the holding cost per cycle, the authors implicitly assumed that the returned items were not replaced by good quality items. In this note, we first point out the contradiction. Then we fix this flaw and develop a corrected EOQ.