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.

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.