Closed-form equations for optimal lot sizing in deterministic EOQ models with exchangeable imperfect quality items

In this paper, the optimal lot size for batches with exchangeable imperfect items is derived where the delay time for the exchange process depends on the quantity of imperfect items. this delay in exchange may or may not lead into shortage. the initial received lot is 100% screened. after the screening process, an order to exchange defective products takes place. the imperfect items are held in buyer's warehouse until the arrival of the exchange lot from the supplier for which, after another 100% screening process, imperfect items are sold at a lower price in a single batch. two possible situations in which 1) there will not be any shortage, and 2) there will be a shortage that is fulfilled before the end of the replenishment cycle, are investigated. proper mathematical models are developed and closed-form formulae are derived. numerical examples are provided not only to demonstrate application of the proposed model, but also to analyze and compare the results obtained employing the proposed model and the ones gained using the classical economic order quantity model.