Inventory Rationing for Multiple Class Demand under Continuous Review

We consider how a firm should ration inventory to multiple classes in a stochastic demand environment with partial, class-dependent backlogging where the firm incurs a fixed setup cost when ordering from its supplier. We present an infinite-horizon, average cost criterion Markov decision problem formulation for the case with zero lead times. We provide an algorithm that determines the optimal rationing policy, and show how to find the optimal base-stock reorder policy. Numerical studies indicate that the optimal policy is similar to that given by the equivalent deterministic problem and relies on tracking both the current inventory and the rate that backorder costs are accumulating. Our study of the case of non-zero lead time shows that a heuristic combining the optimal, zero lead time policy with an allocation policy based on a single-period profit management problem is effective.