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中文摘要：
在已有动态批量决策问题的基础上,考虑了再制造与外包这两个因素建立了单产品的再制造批量决策模型。对考虑外包的单产品再制造批量决策问题最优解的性质进行了讨论,在此基础上利用动态规划的思想给出了时间复杂性为O（T4）的算法,并用C＋＋实现了本算法,实验表明本算法是有效的。
英文摘要：
The paper addresses the single item dynamic lot sizing problem for systems with remanufacturing and outsourcing.The demand and return amounts are deterministic over the finite planning horizon.Demand may be satisfied by manufactured new items or remanufactured items or outsourcing,but it cannot be backlogged.The objective is to determine those lot sizes for manufacturing,remanufacturing and outsourcing that minimize the total cost composed of holding cost for returns and manufactured/remanufactured products,setup costs,and outsourcing cost.We prove several properties of an optimal solution and present exact polynomial time dynamic programming algorithm,which the complexity is O（T4）.
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