Inventory control in production–inventory systems with random yield and rework: The unit‐tracking approach

This paper considers a single‐stage make‐to‐stock production–inventory system under random demand and random yield, where defective units are reworked. We examine how to set cost‐minimizing production/order quantities in such imperfect systems, which is challenging because a random yield implies an uncertain arrival time of outstanding units and the possibility of them crossing each other in the pipeline. To determine the order/production quantity in each period, we extend the unit‐tracking/decomposition approach, taking into account the possibility of order‐crossing, which is new to the literature and relevant to other planning problems. The extended unit‐tracking/decomposition approach allows us to determine the optimal base‐stock level and to formulate the exact and an approximate expression of the per‐period cost of a base‐stock policy. The same approach is also used to develop a state‐dependent ordering policy. The numerical study reveals that our state‐dependent policy can reduce inventory‐related costs compared to the base‐stock policy by up to 6% and compared to an existing approach from the literature by up to 4.5%. From a managerial perspective, the most interesting finding is that a high mean production yield does not necessarily lead to lower expected inventory‐related costs. This counterintuitive finding, which can be observed for the most commonly used yield model, is driven by an increased probability that all the units in a batch are either of good or unacceptable quality.