Lot sizing with a Markov production process and imperfect items scrapped

This paper considers an inventory system within the economic order quantity (EOQ) model framework under random supply. The production process can go ‘out-of-control’ with a constant probability and start producing imperfect quality items. Such a system has been studied in the literature under the assumption that defective items are reworked instantaneously and returned to inventory. In some situations, imperfect quality items are not necessarily defective and are removed from the inventory to be used elsewhere. This paper develops two models where imperfect items are removed from inventory. The first model finds the expected cost and optimal lot size assuming that imperfect quality items are removed from inventory at no cost. The second model assumes that batches of imperfect quality are consolidated and shipped together due to economies of scale in shipping. Analytical and numerical results are developed for both models revealing several managerial insights.