Evaluation and optimization of installation base-stock policies in supply chains with compound poisson demand

In this paper, we establish an exact framework for a class of supply chains with at most one directed path between every two stages. External demands follow compound Poisson processes, the transit times are stochastic, sequential, and exogenous, and each stage controls its inventory by an installation base-stock policy under continuous review. Unsatisfied demand at each stage is fully backordered. This class of supply chains includes assembly, distribution, tree, and two-level general networks as special cases. We characterize the stockout delay for each unit of demand at each stage of the supply chain by developing an exact and unified approach that applies to various network topologies. We also present tractable approximations and decompositions that facilitate efficient evaluation and optimization (up to the approximations) of the base-stock policies in industry-size problems with a tree structure. We demonstrate the effectiveness of the solution by numerical studies.