Inbound replenishment and outbound dispatch decisions under hybrid shipment consolidation policies: An analytical model and comparison

We investigate operational decisions in a distribution warehouse facing stochastic demand and incurring fixed and linear transportation costs for the inbound inventory replenishment and outbound dispatch decisions. In order to realize scale economies associated with transportation both on the outbound and inbound sides, dispatch schedules and replenishment decisions at the warehouse must be synchronized over time. Immediate delivery policies on the outbound side are not financially viable because outbound dispatch operations will benefit from temporal shipment consolidation. Our focus in this setting is the analytical modeling of hybrid shipment consolidation policies and their comparison to the time-based and quantity-based counterparts. To this end, we propose analytical (exact and approximate) methods to compute and compare the cost under hybrid policies relative to its alternatives. Since shipment consolidation impacts customer waiting and inventory holding, we also investigate the average delay per order and average inventory per time unit as two important metrics of the distribution operation’s performance, along with the annual cost. We compare these metrics among the alternative under hybrid, time-based, and quantity-based policies. The comparison then allows us to offer an explicit analytical comparison of long-run average cost under these three policies without needing to solve the corresponding optimization problems. Notably, our results offer an analytical characterization of relative cost performance (vis-a-vis the numerical comparison available in the literature) and demonstrate the implications of alternative shipment consolidation policies regardless of the values of model parameters. The results are of practical value in the context of the design and operation of an integrated framework for inventory-transportation systems.