Optimality of base-stock and (s, S) policies for inventory problems with information delays

Information delays exist when the most recent inventory information available to the inventory manager (IM) is dated; namely, the IM observes only the inventory level of an earlier period. We introduce information delays into the standard multiperiod stochastic inventory problem with backorders. We consider two types of information delays: (i) a constant delay and (ii) a random delay. We define an appropriate reference inventory position, which is a sufficient statistic for finding the optimal order quantity. We show that the optimal ordering policy is of base-stock type with respect to the reference inventory position and is of (s, S) type if there is also a fixed cost of ordering.