Abstract: This paper studies an inventory rationing in a new sboy problem with multiple customer class. The customer classes are distinguished by their pur chasing price,and the firmeither fulfills demand or denies the demand.Through discrediting the selling season into a large number of smaller intervals and using a finite difference equation to approximate the optimality equation,this paper charact erizes the retailer's optimal rationing policy,which is depended on the inventory level and rest time.Under the optimal rationing policy,the expected profit function is concave in the order quantity,and there exists an optimal order quantity to maximize the expected profit.Through comparing with the First-Come-First-Served(FCFS) policy,the numerical analyses illustrates that the inventory rationing policy can improve the firm's profit significantly.This is because that the retailer can obtain more profit from the profit able customers by ensuring the high fill rate.Mean time,the order quantity under rationing policy is less than that under the FCFS policy,and then the retailer can benefit from the rationing policy by saving the purchasing cost and holding cost.

Key words: multiple customer classes, new sboy problem, inventory rationing, dynamic programming