An EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns

In practice the items received in a lot may contain defective items, and the screening process to eliminate the defective items may involve both a Type I and a Type II error. Due to the defective items and the inspection errors, shortages may sometimes occur. In this paper, we develop an economic order quantity model with imperfect quality items, inspection errors, shortage backordering, and sales returns. A closed form solution is obtained for the optimal order size, the maximum shortage level, and the optimal order/reorder point. If shortages are not allowed, we adopt the order overlapping scheme proposed by Maddah et al. (2010) (Computers and Industrial Engineering. 58 (4), 691–695.) to develop an EOQ model to prevent shortages during the screening process. Numerical examples show the impacts of the defective probability, the inspection errors, and the holding and backordering costs on the optimal solution.