  We consider a distribution warehouse where both the inbound inventory
replenishment and outbound dispatch decisions are subject to fixed (as well as
per-unit) transportation charges and demand is stochastic. In order to realize
scale economies associated with transportation operations both on the outbound
and inbound sides, dispatch schedules must be synchronized over time with
inventory replenishment decisions. An immediate delivery policy on the outbound
side does not make economic sense because outbound dispatch operations and
costs will benefit from a temporal shipment consolidation policy. Our
particular interest in this setting is the exact modeling and analysis of
hybrid shipment consolidation policies, in comparison to the time- and
quantity-based counterparts. Since shipment consolidation prolongs customer
waiting and inventory holding, we investigate average delay penalty per order
and average inventory per time unit as critical measures of performance of the
distribution operation, along with the annual cost. By fixing the expected
inbound replenishment and outbound dispatch frequencies, we compare these
measures among the alternative ways of operation under hybrid, time-based, and
quantity-based policies. This comparison then lends itself to an explicit
analytical comparison of average costs under these three policies, without a
need for solving the corresponding optimization problems.
