In the paper, open shop scheduling problems with the objective to minimize the makespan and fixed or proportionally deteriorating operation processing times are considered. We solve the problems using three rules which are modifications of the Longest Alternate Processing Time (LAPT) rule that earlier was proved to be optimal for two-machine open shop scheduling problem with the same objective and fixed operation processing times. We prove that the first of the modified rules is optimal for two-machine open shop scheduling problem with proportionally deteriorating operation processing times. We also show, based on results of conducted numerical experiments, that the next two modified rules generate near-optimal schedules for three-machine open shop problems, regardless whether operation processing times are fixed or proportionally deteriorating.

在本文中，考虑了以最小化制造时间和固定或成比例恶化的操作处理时间为目标的开放式车间调度问题。我们使用三个规则对问题进行解决，这三个规则是对最长备用处理时间（LAPT）规则的修改，该规则被证明更适用于目标时间相同且操作处理时间固定的两台机器的开店调度问题。我们证明，修改后的规则中的第一个规则对于两台机器的开店调度问题是最优的，并且操作处理时间成比例地变差。根据进行的数值实验的结果，我们还表明，接下来的两个修改规则生成了针对三台机器开店问题的接近最优的计划，无论操作处理时间是固定的还是成比例地恶化。