Multi-item inventory systems with nonzero lead-times and probabilistic resource constraints

The common resource constraint for inventory systems is a linear resource constraint which may result in high operating costs in multi-item (R,Q) inventory systems. This paper presents an analysis of multi-item (R,Q) inventory systems with probabilistic resource constraints to minimize the long-run average system cost. Several useful properties of general multi-item (R,Q) inventory systems with nonzero lead-times and probabilistic constraints are derived based on the convexity of the cost function and the probability distribution of the inventory level. These properties serve as the foundation for an efficient polynomial heuristic algorithm for finding the parameters of general multi-item (R,Q) policy inventory systems. An example shows that the probabilistic resource constraint outperforms the standard linear resource constraint.