Optimal Inventory Policy for Systems with Demand Cancellations

We analyze a periodic review inventory model in which all demands have to be reserved with a one-period leadtime. During the reservation period, some of the reservations may be cancelled. As a result, the reservation information is not perfectly reliable. Our objective is to determine the optimal replenishment policy for this inventory model. We show that the cost function is convex and the optimal policy is a "reorder-up-to" type of policy. This policy stipulates that unless the initial on-hand inventory is lower than the reorder-up-to level, an order should be made to raise the inventory level to the reorder-up-to level. Furthermore, this reorder-up-to level is a function of the amount of reserved demand. The single- and multiple-period cases are studied. Finally, we consider the infinite-horizon case and show that results from the finite-horizon case converge to the infinite-horizon case. The expression for solving the optimal policy parameter is also derived.