Computing (r, Q) policy for an inventory system with limited sharable resource

This paper deals with inventory systems with limited resource for a single item or multiple items under continuous review (r, Q) policies. For the single-item system with a stochastic demand and limited resource, it is shown that an existing algorithm can be applied to find an optimal (r, Q) policy that minimizes the expected system costs. For the multi-item system with stochastic demands and limited resource commonly shared among all items, an optimization problem is formulated for finding optimal (r, Q) policies for all items, which minimize the expected system costs. Bounds on the parameters (i.e., r and Q) of the optimal policies and bounds on the minimum expected system costs are obtained. Based on the bounds, an algorithm is developed for finding an optimal or near-optimal solution. A method is proposed for evaluating the quality of the solution. It is shown that the algorithm proposed in this paper finds a solution that is (i) optimal/near-optimal and/or (ii) significantly better than the optimal solution with unlimited resource.