Optimal production and inventory policy for multiple products under resource constraints

We show that a modified base-stock policy is optimal for multiproduct, infinite-horizon production-inventory systems, where demand for the products is random and the products share a finite resource every period. We characterize the optimal policy for the case of homogeneous products. Because of the difficulty in computing the optimal base-stock levels for the heterogeneous case, we propose a heuristic that is simple enough for practical applications. We present numerical results that suggest that the heuristic yields near-optimal solutions.