Abstract: Nowadays, it is common for suppliers to be separated from their buyers by great distances. This means that, if some items in the lot turn out to be defective, the distance makes it uneconomical to order replacements from the original supplier. Moreover, both Type I and Type Ⅱ errors may occur in the screening process for eliminating defective items and the combination of defective items and inspection errors may lead to shortages. Working with these assumptions, this paper develops two distinct models. Under the first model, defective items are repaired by a local repair shop subject to a repair charge and a mark-up margin. Under the second model, a local supplier replaces the defective with good ones, but at a higher cost. The expected total profit per cycle is developed, together with the expected cycle time, and, employing the renewal reward theorem, the objective function is derived, from which the optimum values are obtained for the order and shortage quantities. The paper presents numerical results and a discussion for both models. The study finds that repairing defective items generally leads to greater total profit than purchasing local replacements.

Key words: Economic order quantity, Inspection errors, Optimization, Gaussian numerical integration, Shortages, Repair/emergency purchase