Storage-space capacitated inventory system with (r, Q) policies

We deal with an inventory system with limited storage space for a single item or multiple items. For the single-item system, customers' demand is stochastic. The inventory is controlled by a continuous-review (r, Q) policy. Goods are replenished to the inventory system with a constant lead time. An optimization problem with a storage-space constraint is formulated for computing a single-item (r, Q) policy that minimizes the long-run average system cost. Based on some existing results in the single-item (r, Q) policy without a storage-space constraint in the literature, useful structural properties of the optimization problem are attained. An efficient algorithm with polynomial time computational complexity is then proposed for obtaining the optimal solutions. For the multi-item system, each item possesses its particular customers' demand that is stochastic, its own (r, Q) policy that controls the inventory, and its individual lead time that is constant. An important issue in such inventory systems is the allocation of the storage space to the items and the values of r and Q for each item. We formulate an optimization problem with a storage-space constraint for multi-item (r, Q) policies. Based on the results in the single-item (r, Q) policy with a storage-space constraint, we find useful structural properties of the optimization problem. An efficient algorithm with polynomial time computational complexity is then proposed for obtaining undominated solutions.