On the Stochastic Inventory Problem under Order Capacity Constraints *

We consider the single-item single-stocking location stochastic inventory system under a fixed ordering cost component. A long-standing problem is that of determining the structure of the optimal control policy when this system is subject to order quantity capacity constraints; to date, only partial characterisations of the optimal policy have been discussed. An open question is whether a policy with a single continuous interval over which ordering is prescribed is optimal for this problem. Under the so-called "continuous order property" conjecture, we show that the optimal policy takes the modified multi -(s, S) form. Moreover, we provide a numerical counterexample in which the continuous order property is violated, and hence show that a modified multi -(s, S) policy is not optimal in general. However, in an extensive computational study, we show that instances violating the continuous order property do not surface, and that the plans generated by a modified multi -(s, S) policy can therefore be considered, from a practical standpoint, near-optimal. Finally, we show that a modified (s, S) policy also performs well in this empirical setting. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )