Economic order quantity for imperfect quality items under inspection errors, batch replacement and multiple sales of returned items

In classical inventory control problems, it is usually assumed that all of items are of perfect quality, and the inspection process works perfectly well. However, in practice, the order lots often contain imperfect quality items, and the inspection process, for recognition of these items, is not necessarily error-free. In this article, we extend the economic order quantity model under imperfect quality items where the inspection process involves type I and II errors. The type I error can lead to recognition of perfect quality items as defective, while the type II error can lead to delivery of imperfect quality items to customers even for several consecutive times. We present two cases depending on the length of special inspection process and determine optimal order sizes, analytically, for maximizing total profit per unit time for both cases. A numerical example is provided to compare two cases and a sensitivity analysis is discussed to assess the effect of main parameters on the total profit per unit time.