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.