Optimal Centralized Ordering Policies in Multi-Echelon Inventory Systems with Correlated Demands

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Abstract
This paper treats a depot-warehouse system in which demand occurs at the warehouse or retail level. This work differs from a number of other studies in that we allow item demands to be correlated both across warehouses and also correlated in time. Our motivation for this generalization arises from our experience with an actual system of this type used by a major national producer and distributor of consumer products. We observed both high correlations between successive monthly demands (around 0.7) and correlations between demands for an item at different locations (also about 0.7) in a given time period. We derive an explicit expression for the optimal safety stock as a function of the level of correlation through time. The analysis requires two assumptions: 1) the allocation assumption and 2) the equal coefficient of variation assumption. (Similar assumptions have been used by other researchers.) Finally, numerical evaluations are included to illustrate the impact of the various magnitudes of correlation.

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