EPQ models for items with imperfect quality and one-time-only discount

In developing countries with many OEMs (Original Equipment Manufacturer), self-producing companies sometimes face a one-time-only discount for the same products offered by the OEMs. Making such a special order from the OEM may or may not be beneficial to the manufacturer who usually produces himself. In this paper, EPQ (economic production quantity) models were developed to evaluate the optimal make-or-buy decisions when such a manufacturing company faces a one-time-only discount offered by an OEM. To reflect real situation, imperfect quality of both self-produced and purchased products was also considered in the models. Conditions under which the manufacturer should place a special order from the OEM and related optimal ordering quantities were obtained. A numerical example was presented to illustrate the managerial insights of the models.