IESE Research Papers,
IESE Business School

Abstract: 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.

Keywords: multi-echelon; optimal control; unit-tracking decomposition

35 pages, February 1, 2011

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