A lost-sale inventory system with dual supply and multiple demand classes

We deal with an inventory system that serves multiple demand classes and procures from two suppliers. Inventory replenishments and rationing decisions have to be made in each period. We show that the optimal rationing decision is characterized by a set of critical levels, and the optimal decision to replenish from the faster supplier follows a modified base-stock policy. For the optimal decision to replenish from the slower supplier, structural results on monotonicity with respect to the inventory state are derived. We also examine the performances of the system by a numerical experiment.