A characterization of optimal base-stock levels for a continuous-stage serial supply chain

In this paper, we present a continuous model to optimize multi-echelon inventory management decisions under stochastic demand. Observing that in such continuous system it is never optimal to let orders cross, we decompose the general problem into a set of single-unit sub-problems that can be solved in a sequential fashion. When shipping and inventory holding costs are linear in the stage, we show that it is optimal to move the unit associated with the k-th next customer if and only if the inventory unit is held in an echelon located within a given interval. This optimal policy can be interpreted as an echelon base-stock policy such that the base-stock is initially increasing and then decreasing in the stage. We also characterize the optimal policy when costs are piecewise-constant. Finally, we study the sensitivity of the optimal base-stock levels to the cost structures.