We refer to demand information as current when the information is based on current data such as
point of sales information and when it does not provide future information such as a promotion
scheduled for next period, or advance order information. Here, we briefly review the classical single
location inventory literature as a bridge to more recent work that incorporates the dynamic nature
of demand information, such as forecast updates.
Early inventory models addressed the problem of minimizing ordering, holding, and backlogging
costs for a single product at a single location over either a finite or an infinite horizon. Demand
uncertainty is modeled as independent and identically distributed over time, i.e., demand Dt at each
period t is an iid random variable. This modeling assumption uses current demand information.
In particular, the sequence of events for such a system is as follows. At the beginning of each
period t, the manager reviews on-hand inventory It, any backorders Bt and the pipeline inventory.
The manager decides whether or not to produce zt 0. She incurs a non-stationary production
cost of Kt(zt) + ct(zt), where (z) = 1 if z > 0, Kt is the fixed production cost, and ct is the
variable production cost. The production initiated at period t−L is added to the inventory, that is,
L periods are required to complete the production. Demand Dt is observed. The demand for period
t is satisfied through on-hand inventory; otherwise it is backordered. The manager incurs holding
and penalty costs based on end-of-period net inventory.