中文摘要：

提出了一类制造企业的联合成本优化问题，将企业的产品制造环节和配送环节进行协同运作．实现供应链环境下的联合调度．在生产环节，考虑一类典型的差异分批制造模式，即待加工的作业尺寸有差异，而批处理设备的容量确定，设备环境为多台并行设备；在配送环节，企业采用自有车辆进行运输，车辆具有相同的运输能力；若完工的作业在当前无可用车辆进行配送。则转入产成品库存；联合成本为生产、库存和配送三阶段的总成本．本文首先构造了基于整数规划的数学模型，证明了联合成本的最小化问题是强NP-hard问题；然后设计了多项式时间的近似算法，分析了算法的时间复杂性，并证明了算法的求解性能．

英文摘要：

A class of problems for manufacturers are proposed to minimize joint cost. Production and outbound distribution are combined to achieve a joint scheduling in supply chain. In the production process, the manu- facturers have identical parallel batching machines to process arbitrary-size jobs. The machines have a fixed capacity in size and the total size of jobs in a batch cannot exceed the machine capacity. In the distribution process, the manufacturers deliver the products using their own vehicles and the vehicles have identical trans- port capacities. If there are no available vehicles to deliver the products, they should be put in inventory. The total cost consists of the production cost, the distribution cost and inventory cost. An integer programming model of the problem is presented and the problem under investigation is shown to be NP-hard in the strong sense. Then a polynomial time algorithm is provided. The time complexity and performance guarantee of the proposed algorithm are analyzed.