Probabilistic Service Level Guarantees in Make-to-Stock Manufacturing Systems

We consider a realistic model of a multiclass make-to-stock manufacturing system. External demand for each product class is met from the available nished goods inventory; unsatis ed demand is backlogged. The objective is to devise a production policy that minimizes inventory costs subject to guaranteeing stockout probabilities to stay bounded above by given constants j , for each product class j (service level guarantees). Such a policy determines whether the facility should be producing (idling decisions), and if it should, which product class (sequencing decisions). We analyze a corresponding uid model of the system to take sequencing decisions and employ large deviations techniques to take idling ones. We consider both linear and quadratic inventory cost structures to obtain a priority-based and a generalized longest queue rst-based production policy, respectively. Our analysis is general enough to accommodate autocorrelated demand and service processes, both critical features of modern failure-prone manufacturing systems.