The paper considers scheduling on parallel machines under the constraint that some pairs of jobs cannot be processed concurrently. Each job has an associated weight, and all jobs have the same deadline. The objective is to maximise the total weight of on-time jobs. The problem is known to be strongly NP-hard in general. A polynomial-time algorithm for scheduling unit execution time jobs on two machines is proposed. The performance of a broad family of approximation algorithms for scheduling unit execution time jobs on more than two machines is analysed. For the case of arbitrary job processing times, two integer linear programming formulations are proposed and compared with two formulations known from the earlier literature. An iterated variable neighborhood search algorithm is also proposed and evaluated by means of computational experiments.

翻译：文件考虑了平行机器的时间安排,其限制是,有些工作不能同时处理。每个工作都有相关的重量,所有工作都有相同的期限。目标是最大限度地提高实时工作的总重量。问题一般是相当严重的NP硬的。提出了两台机器上单位执行时间工作时间安排的多元时间算法。分析了两个以上机器上各组单位执行时间工作时间安排的近似算法。在任意工作处理时间的情况下,提出了两个整线性编程配方,与先前文献中已知的两种配方相比较。还提出并用计算实验方法评价了循环社区搜索算法。