Dynamic inventory rationing is considered for systems with multiple demand classes, stationary stochastic demands, and backordering. In the literature, dynamic programming has been often applied to address this type of problems. However, due to the curse of dimensionality, computation is a critical challenge for dynamic programming. In this paper, an innovative two-step approach is proposed based on an idea similar to the certainty equivalence principle. First the deterministic inventory rationing problem is studied, where the future demands are set to be the expectation of the stochastic demand processes. The important properties obtained from solving the problem with the KKT conditions are then used to develop effective dynamic rationing policies for stochastic demands, which gives closed-form expressions for dynamic rationing thresholds. These expressions are easy to calculate and are applicable to any number of demand classes. Numerical results show that the expressions are close to and provide a lower bound for the optimal dynamic thresholds. They also shed light on important managerial insights, for example, the relation between different parameters and the rationing thresholds. 
Multi-class dynamic inventory rationing with stochastic demands and backordering