  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 are extremely rare in practice, and that the plans generated by a
modified multi-$(s,S)$ policy can therefore be considered, for all practical
purposes, optimal. Finally, we show that a modified $(s,S)$ policy also
performs well in practice.
