#### Optimal Ordering Policies for Inventory
Problems with Dynamic Information Delays

**Abstract: **Information delays exist when the most
recent inventory information available to the Inventory Manager (IM) is dated.
In other words, the IM observes only the inventory level that belongs to an
earlier period. Such situations are not uncommon, and they arise when it takes
a while to process the demand data and pass the results to the IM. We introduce
dynamic information delays as a Markov process into the standard multi-period
stochastic inventory problem with backorders. We develop the concept of a *
reference inventory position*. We show that this position along with the
magnitude of the latest observed delay and the age of this observation are
sufficient statistics for finding the optimal order quantities. Furthermore, we
establish that the optimal ordering policy is of state-dependent-base-stock type
with respect to the reference inventory position (or state-dependent (*s,S*)
type if there is a fixed ordering cost). The optimal base stock and (*s,S*)
levels depend on the magnitude of the latest observed delay and the age of this
observation. Finally, we study the sensitivity of the optimal base stock and
the optimal cost with respect to the sufficient statistics.