Summary: Periodic review systems are commonly employed by distributors and retailers to replenish their inventories (for example, to co-ordinate in-bound transportation). It is also often the case that vendors specify minimum purchase quantities for physical (for example, packaging) or strategic reasons. When inventory systems recommend order quantities below the prescribed minimum, a decision must be made on whether or not to order. We describe how this environment can be modelled, and employ an extensive factorial experiment involving a simulation to demonstrate situations in which a common simple `rounding up' decision rule performs poorly. In this paper, we discuss financial implications and implementation issues.