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中文摘要：
当企业自身能力不能满足需求时考虑外包，可以有效提高企业的竞争力。一种带能力外包的多产品动态经济批量问题得以提出，并设定外包能力使用价格较高且费用时变。建立混合整数规划模型，通过约束松弛与模型分解，设计出一个基于拉格朗日松弛理论的启发式算法进行模型求解。大量随机实验表明，无论解的质量还是求解时间都表现较好。
英文摘要：
Subcontracting capacity to third parties has become a prevalent practice for improving an enterprise＇s competitive power and agility. In the problem, each order placed in a period is immediately shipped by some containers in the period and the total freight cost is proportional to the number of containers used. If the number of enterprisers containers is insufficient, then the enterprise needs to contract additional transportation capacity on the spot market, where the price of single container is higher and time-varying. The simultaneous determination of the lot sizes and the transportation policy that minimizes the total costs, including ordering cost, inventory holding cost and freight cost, is dealt with. As the problem is NP-hard, a lagrangian-based heuristic algorithm is proposed to compute lower and upper bounds, of which the comprehensive computational experiments show the compelling performance in terms of quality and speed.
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