提出了公共交货期窗口下提前 /拖期惩罚的多台不同设备情形的零件排序模型 .在分析相应单机问题最优排序和最优交货期性质的基础上 ,证明该多机零件问题实际上蕴含着使系统 makespan达最小的多机零件排序问题 .由于使系统 makespan达最小的并行多机零件排序问题已被证明是 NP完全问题 ,因此提出了求解该零件排序问题的一个启发式算法 ,该算法计算复杂性低且对并行多机零件排序问题同样适用 .最后给出了两个数值例子 . A part sorting model for multiple equipments with a lead time/trail penalty under the common delivery window was proposed. Based on the analysis of the optimal ordering of the corresponding single machine problem and the nature of the optimal delivery date, the multi-machine parts problem was proved to be practical. The implied problem is to minimize the multi-machine part scheduling problem that makes the system makespan. Because the problem of making the system makespan the smallest concurrent multi-machine parts sequencing problem has been proved to be a NP-complete problem, a heuristic algorithm is proposed to solve the part scheduling problem. The computational complexity of the algorithm is low and the parallel multi-machine parts scheduling problem is also applicable. Finally, two numerical examples are given.