Joint shipment consolidation and inventory decisions in a two-stage distribution system

•This problem is motivated by a real-world problem faced by an industrial distributor.•Joint transportation and inventory decisions in a two-stage supply chain are analyzed.•An exact optimization technique to compute the optimal parameters is proposed.•Consolidation time can be readjusted to minimize the overall expected cost.•The DC acts as a cross-docking facility if inventory and dispatching costs are high. This study is motivated by a problem that an industrial distributorship faced while distributing automotive spare parts to service and repair centers. Considering the problem encountered, we present an analytical model for joint inventory and shipment consolidation decisions in a two-stage distribution system with a single distribution center, multiple non-identical retailers, and an outside supplier. The retailers face stochastic end-customer demand and use continuous review to replenish inventories. On the other hand, the distribution center uses a periodic review policy and employs a time-based shipment consolidation policy to dispatch retailers’ accumulated orders at the end of each consolidation cycle. We present an exact optimization technique to compute the optimal replenishment quantity at the distribution center, order-up-to level at retailers, and a shipment consolidation cycle length to measure the effects of inventory at retailers on the overall performance. Finally, we perform numerical experiments to measure the impact of various parameters on the overall distribution system.