Critical level rationing in inventory systems with continuously distributed demand

This paper analyzes the use of a constant critical level policy for fast-moving items, where rationing is used to provide differentiated service levels to two demand classes (high priority and low priority). The previous work on critical level models, with either a continuous or periodic review policy, has only considered slow-moving items with Poisson demand. In this work, we consider a continuous review (Q, r, C) policy with two demand classes that are modeled through continuous distributions, and the service levels are measured by the probability of satisfying the entire demand of each class during the lead time. We formulate a service level problem as an non-linear problem with chance constraints for which we optimally solve a relaxation obtaining a closed-form solution that can be computed easily. For instances, we tested, computational results show that our solution approach provides good-quality solutions that are on average $$0.3~\%$$ 0.3 % from the optimal solution.