The objective of this paper is to minimize both the makespan and the total completion time. Since parallel-machine scheduling which contains the function constraint problem has been a new issue, this paper explored two parallel-machine scheduling problems with function constraint, which refers to the situation that the two machines have a same function but one of the machines has another. We pointed out that the function constraint occurs not only in the manufacturing system but also in the service system. For the makespan problem, we demonstrated that it is NP-hard in the ordinary sense. In addition, we presented a polynomial time heuristic for this problem and have proved its worst-case ratio is not greater than 5/4. Furthermore, we simulated the performance of the algorithm through computational testing. The overall mean percent error of the heuristic is 0.0565%. The results revealed that the proposed algorithm is quite efficient. For the total completion time problem, we have proved that it can be solved in time.

中文翻译：

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具有功能约束的两个并行机调度问题

本文的目的是最小化制造时间和总完成时间。由于包含功能约束问题的并行机调度已成为一个新问题，因此本文探讨了两个具有功能约束的并行机调度问题，这是指两台机器具有相同功能但一台机器具有另一台机器的情况。 。我们指出，功能约束不仅发生在制造系统中，而且发生在服务系统中。对于制造期问题，我们证明了从一般意义上讲它是NP难的。此外，我们提出了针对该问题的多项式时间启发式方法，并证明了其最坏情况比率不大于5/4。此外，我们通过计算测试来仿真算法的性能。启发式方法的总体平均百分比误差为0.0565％。结果表明，该算法是有效的。对于总完成时间问题，我们证明了可以解决 时间。