A dynamic inventory rationing problem with uncertain demand and production rates

We investigate the structural properties of a finite horizon, discrete time single product inventory rationing problem, where we allow random replenishment (production) opportunities. In contrast to the standard models of dynamic capacity control in revenue management or production/inventory systems, we assume that the demand/production rates are not known with certainty but lie in some interval. To address this uncertainty, we formulate a robust stochastic dynamic program and show how the structural properties of the optimal policy propagate to the robust counterpart of the problem. Further, we explore how the optimal policy changes with respect to the uncertainty set. We also show that our results can be extended to certain alternative robust formulations.