中文摘要：

考虑一个供应商以面向库存生产的方式制造某个产品出售给多个客户.客户以批量进行订货,其到达供应商处的需求若未能即时满足则视为积欠订货.供应商根据每个客户的积欠订货成本将其划分为若干个需求类.文中根据客户每次订货是否可分批交货,分别提出了当客户订货可分割和不可分割时供应商的最优生产和库存配给策略.分析表明客户订货是否可分割对于供应商的生产控制策略没有影响,但会影响到库存配给策略.另外,供应商的最优生产控制策略可用一个取决于系统状态的基准库存水平表示,最优的库存配给策略则用一个多层的取决于状态的配给水平向量表示.数据分析验证了文中最优策略的有效性,同时表明当客户订货不可分割时,相对于高优先权需求,低优先权需求类订货量的增加会引起供应商成本较大幅度的增加.

英文摘要：

This paper considers that a supplier produces and delivers a single product to multiple customers in the form of make-to-stock.Each customer orders in batch size.Incoming orders that are not satisfied immediately are regarded as backorder.The customers can be divided into several demand classes according to their respective backorder costs.Optimal production and inventory rationing policies of the supplier for the cases with and without order split are developed.The analysis shows that there is no effect of order split on the supplier＇s optimal production controlling policy.In addition,the optimal production controlling policy is presented with a state-dependent production base stock level and the optimal rationing policy is represented with a multi-level state-dependent rationing level vector.The effectiveness of the policies is tested by a numerical example.Moreover,numerical results show that the effect of the order size of the less valuable demand class on the supplier＇s cost is larger than that of the more valuable demand class.