An EOQ model with backorders and rejection of defective supply batches

We consider a single-echelon inventory installation under the classical EOQ (with backorders) paradigm to study the effects of supply quality on cost performance. Previous research on imperfect supply quality has focused on variants of the proportional (deterministic or random) yield problem, where supply batches are all accepted and then used, after screening any defects. In this paper we study an alternative setting where, entire supply batches may be defective (below quality standards) and therefore rejected on arrival. Note that such supply flow disruptions are analogous to those considered within the economic order quantity with disruptions (EOQD) area of research. We first present an exact model for the system expected cost and show its convexity. Optimal cost and respective values of the decision variables (i.e. planned order quantity and backorders) are then obtained in a closed form. Interestingly, under perfect supply quality, all expressions reduce to those of classical EOQ. Analytical and computational results reveal the serious impact of inferior supply quality on system cost as well as the sensitivity of the system parameters.