Optimal inspection effort and scheduling for a manufacturing process with repair

Traditional economic models of optimal inspection allocation do not recognize that the inspection and repair activities place an extra burden on a production system. A common result of the traditional models is that the optimal solution takes the form of ‘all or none’ inspection. In this paper, the extra load that inspection and repair present are explicitly modelled for a single stage manufacturing system in which items are processed, possibly inspected, and then repaired, if necessary. First, the optimal inspection effort is determined for the situation when defective items are repaired immediately. Due to the presence of queueing in the model, the optimal solution no longer takes the form of ‘all or none’ inspection. Next, results from the literature on multi-armed bandits are used to optimally schedule the processing and repair tasks jointly with determining the optimal inspection effort.