The Multiperiod Multilocation Inventory Problem

This paper studies the structure of optimal policies in general multiperiod, multilocation inventory problems with proportional costs. It is shown that the multiperiod problem has the same generic form in each period as a one-period problem Hence, properties of the one-period problem are inherited by the multiperiod formulation; in particular the form of the optimal policy can be characterized. In the special case of a Leontief system structure (and for a somewhat more general class) it is shown that base-stock policies are optimal for certain initial states. For the stationary problem some results are derived about the monotonicity of the sequence of base stock vectors.