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 multiperiod stochastic inventory problem with backorders. We develop the concept of a reference inventory position. We show that this position 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.

Keywords: dynamic information delays, partial observations, stochastic inventory problem, base-stock policy, (s, S) policy, inventory models, incomplete information, sufficient statistics

JEL Classification: C61, M11, D81, D83