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Managing Capacitated Multiechelon Systems with Domain-Optimal Policies

We consider a multiechelon system with stochastic demand and processing capacity constraints at each stage. When the smallest capacity is at the lowest echelon, we identify an inventory domain, a subset of the feasible state space characterized by a high level of pipeline inventory, where this system, in the spirit of Clark and Scarf (1960), preserves additive convexity of the objective function. We show the form of the optimal policy to be a state-­‐dependent echelon basestock policy, whose novel feature is that the optimal inventory decision at each stage is determined (only) by echelon inventories upstream of that stage, in a piecewise linear manner. We conduct a numerical study to evaluate the heuristic performance of this policy for a capacitated system with no pipeline inventory constraints. The results demonstrate that the policy yields an excellent approximation to the optimal cost across a wide range of model parameters at high system utilizations.