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

We consider a model of a multiclass make-to-stock manufacturing system. External demand for each product class is met from the available finished goods inventory; unsatisfied 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 ε_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). Approximating the original system, we analyze a corresponding fluid model to make sequencing decisions and employ large deviations techniques to make idling ones. We consider both linear and quadratic inventory cost structures to obtain a priority-based and a generalized longest queue first-based production policy, respectively. An important feature of our model is that it accommodates autocorrelated demand and service processes, both critical features of modern failure-prone manufacturing systems.