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 the items are of perfect quality and the inspection process works perfectly well. however, in practice, the order lots often contain imperfect items, and the inspection process is not necessarily error-free. in this article, we extended the economic order quantity model under imperfect items where the inspection process involves type-i and -ii errors. the type-i error can lead to recognition of perfect items as defective, while the type-ii error can result in the delivery of imperfect items to customers. in the proposed inventory problem, the customers who receive and return imperfect items wait for replacement with perfect items as a batch at the end of a special inspection process. besides, the imperfect quality items are sold out as discounted items. our problem considers more than one sales per cycle for returned items from market which causes a reduction in the inventory costs. we presented two cases depending on the length of the special inspection process. a numerical example was provided to compare two cases and a sensitivity analysis was discussed to assess the effect of the main parameters on the total profit.