A Comparison of the Optimal Costs of Two
Canonical Inventory Systems
Ganesh Janakiraman*, Sridhar Seshadri*,
and George Shanthikumar
*
We
compare two inventory systems, L and B. In the former, excess demand is lost
while excess demand is backordered in the latter. Both systems are reviewed
periodically, and they experience the same sequence of identically and
independently distributed random demands. Holding and shortage costs are
considered. When the cost parameters in one system are identical to those in
the other, we demonstrate that the optimal expected cost for managing L is
lower than that for managing B. The proof is based on a novel application of
convex ordering and a construction of a sequence of inventory systems
connecting L and B. When the shortage cost parameters are unequal between the
two systems, we establish a relationship between these parameters that ensures
that the reverse inequality is true.