The value of joint decision-making in an inventory–production system with random yield and imperfect information

We study a production–inventory system for a single type of product with random demand and random yield. We consider a production process that suffers from quality problems where non-conforming units cannot be used to replenish the inventory. The portion of non-conforming units depends on the condition of the production process. We distinguish between two process states with different probabilities to produce a non-conforming unit. The process state cannot be observed directly but control charts are implemented to gather information. If the chart yields to an alarm, an inspection is performed and the machine is repaired, if necessary. We assume that a periodic review order-up-to policy is applied to replenish the inventory. The decision-maker has to choose the order-up-to level, as well as the sampling interval and the control chart parameters, in order to minimise the costs. We introduce a model, based on a Markov chain, to determine near optimal policy parameters and conduct a simulation study that indicates an excellent performance of the approximation. Our results give insights into the effects of quality control on inventory system performance and show that joint decision-making of the production and inventory department is advantageous.