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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.