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中文摘要：
研究工件排序与转包相联的模型，即制造商从客户处接受一批工件，这些工件既可以由制造商加工，也可以一定费用转包给承包商加工．制造商需要确定被转包的工件集及工件的加工顺序，使得加工费用和转包费用之和为最小．研究制造商为平行机及自由作业，承包商为单机情况下的排序与转包模型，基于动态规划算法给出了近似算法，并分析了该算法的性能比．
英文摘要：
This paper studies models on scheduling with subcontracting options under parallel and open-shop machines. In the models a manufacturer receives a set of jobs from its customers at the beginning of the planning horizon. Each job can be either processed by manufacturer＇s machines in-house or subcontracted to subcontractor＇s machines at costs. The manufacturer needs to determine which orders should be produced in-house and which orders should be subcontracted. Furthermore, it needs to determine a production sched- ule for all orders. The objective is to minimize the sum of production and subcontracting cost. Based on the dynamic programming algorithm, a approximate algorithm with worst-case performance analysis is given for the problems under manufacturer＇s parallel and open shop machines and subcontractor＇s single machine respectively.
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