On the decomposition property for a dynamic inventory rationing problem with multiple demand classes and backorder

In this paper, we study a dynamic inventory rationing problem of a single item with multiple demand classes and backorder. Demand classes are differentiated by their unit backlogging costs. The corresponding dynamic programming problem is multidimensional and computationally challenging. With a novel state transformation, we find that the optimal policy can be described by a nested base stock policy. In particular, we can decompose the value function as the sum of single-variable convex functions. This property breaks the curse of dimensionality and significantly reduces computational effort in computing optimal policies. Our approach allows us to extend the results to systems with ordering, exogenous supply, priority upgrading.