Threshold-based control for make-to-stock models: a synergy between large deviations and perturbation analysis

We consider a model of a make-to-stock manufacturing system. External demand is met from the finished goods inventory; unsatisfied demand is backlogged. We adopt a base-stock production policy which produces if inventory falls below a certain threshold and idles otherwise. We set this threshold to guarantee stockout or delay probabilities to stay below given constants (service level constraints). These can be set by solving a utility maximization problem which trades-off quality of service with expected inventory costs. We combine analytical (large deviations) and simulation-based (perturbation analysis) techniques. We demonstrate that there is a natural synergy between these two approaches