A note on periodic review inventory models with stochastic supplier's visit intervals and fixed ordering cost

Most periodic review models in the inventory literature have assumed a fixed length of the review periods. In this note, we extend the work of Chiang (2008), and consider backlogged and lost-sales periodic review models where the review periods are of a variable length and there is a fixed cost of ordering for replenishment. Assuming that period lengths are independently and identically distributed, we show (using an exact method of computing inventory holding costs) that an (s, S) policy is optimal for the infinite horizon problem. The periodic review policies developed are thus easy to implement. The computation shows that if the fixed cost of ordering is small, one needs to use the proposed periodic policies.