Many inventory control studies consider either continuous review and continuous ordering, or periodic review and periodic ordering. Mixtures of the two are hardly ever studied. However, the model with periodic review and continuous ordering is highly relevant in practice, as information on the actual inventory level is not always up to date while making ordering decisions. This paper will therefore treat this model. Assuming zero fixed ordering costs, and allowing for a non-negative lead time and a general demand process, we first consider a one-period decision problem without salvage cost for inventory remaining at the end of the period. In this setting we derive a base-line optimal order path, described by a simple newsvendor solution with safety stocks increasing towards the end of a review period. We then show that for the general, multi-period problem, the optimal policy in a period is to first arrive at this path by not ordering until the excess buffer stock from the previous review period is depleted, then follow the path by continuous ordering, and stop ordering towards the end to limit excess stocks for the next review period. An important managerial insight is that, typically, no order should be placed at a review moment, although this may seem intuitive and is also the standard assumption in periodic review models. We illustrate that adhering to the optimal ordering path instead can lead to cost reductions of 30–60 percent compared to pure periodic ordering. 
Periodic review and continuous ordering