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Technical Note - On Optimal Policies for Inventory Systems with Batch Ordering

We study a periodically reviewed multiechelon inventory system in series such that order quantities at every stage have to be multiples of a given stage-specific batch size. The batch sizes are nested in the sense that the batch size for every stage is an integer multiple of the batch size for its downstream stage. The problem is that of determining the policy that minimizes the expected discounted sum of costs over a finite horizon. The result is that an echelon (R, nQ) policy is optimal when demands are independent across periods or, more generally, Markov-modulated. We also comment on algorithmic implications of our result and on extensions.