Periodic review inventory models with stochastic supplier's visit intervals

Periodic review inventory models are widely used in practice, especially for inventory systems in which many different items are purchased from the same supplier. However, all periodic review models have assumed a fixed length of the review periods. In practice, it is possible that the review periods are of a variable length. Such periodic systems result mainly from supply uncertainties. For example, the supplier visits the downstream retailers and replenishes inventories for them, but does not always come in constant intervals. This may be because retailers are geographically dispersed in the supply chain, the supplier is in a relatively more powerful position, or the supplier simply does not have a reliable visit schedule. In such situations, the replenishment cycle length is random in nature. In this paper, we use dynamic programming to model such institutional contexts. We assume that the supplier's visit intervals are independently and identically distributed. With a suitable transformation, the backlogged periodic review model derived becomes a standard discrete-time model. The computation shows that ignoring the variability of the supplier's visit intervals can incur extremely large losses, especially if shortage is costly, demand variability is low, and/or the replenishment lead-time is short.