Safety stock positioning in supply chains with stochastic lead times

We study the safety stock positioning problem in single-product multistage supply chains with tree network structures, where each stage controls its inventory using an installation continuous-time base-stock policy. External demands follow independent Poisson processes, and unsatisfied demands at each stage are fully backordered. The processing (e.g., production) cycle times and transportation lead times are assumed to be stochastic, sequential, and exogenously determined. We derive recursive equations for the backorder delays (because of stockout) at all stages in the supply chain. Based on the recursive equations, we characterize the dependencies of the backorder delays across different stages in the network, and develop insights into the impact of safety stock positioning in various supply chain topologies. We present approximations and algorithms to coordinate the base-stock levels in these supply chains, so as to minimize systemwide inventory cost subject to meeting certain service-level requirements of the external customers.