Emergency order replacement of substandard products under economic production quantity model, including shortages and backordering

This paper concerns inventory control under the economic production quantity model, allowing for substandard products and shortages. The imperfect manufacturing system creates a percentage of substandard products, treated as a random variable having a known probability distribution function. All products produced are screened to identify substandard products. It is commonly assumed in the literature that substandard products are subtracted from the inventory for sale as a single batch at a reduced price. However, in some situations, it may be appropriate to repair an item or to obtain a substitute from a local supplier, regardless of its higher price. Restrictions such as production programming may make it impossible to rework substandard products, but the manufacturer has the option of replacing them by purchasing products of good quality from a domestic supplier, though these will normally have a higher unit cost. Three possible cases can occur, depending on the timing of adding emergency-purchased products to the inventory. The paper presents a numerical example and a sensitivity analysis to show how the three cases are applied within the proposed inventory model. [Submitted 24 January 2020; Accepted 22 August 2020]