Periodic review and continuous ordering

There exist many inventory control studies that consider either continuous review & continuous ordering, or periodic review & 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 consider this case of periodic review and continuous ordering. 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 with no salvage cost for inventory remaining at the end of the period. In this setting we derive a base-line optimal order path, which is 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 for some time 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 and possibly counterintuitively, 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 for Normally distributed demand that adhering to the optimal ordering path instead can lead to cost reductions of 30% to 60% compared to periodic ordering, i.e. ordering exclusively at review moments.