State Dependent Maintenance Scheduling

机器退化以及预防性和预测性维护操作在调度文献中已经被考虑了很长一段时间。大多数模型假定机器的退化是时间依赖的，即机器会因使用年限或使用时间而退化。此外，维护操作通常被认为是固定的持续时间，从而导致机器的完全恢复。这些模型忽略了这样一个事实，即机器的恶化可能取决于一些因素，如作业的设置数量，或者更广泛地说，可以通过机器的状态来表示，这可能会受到每个作业的单独影响。例如，在航空领域，飞机的状态可以通过飞行小时数、飞行距离和飞行次数来定义。在前期工作中，申请者开发了三个基本模型。在第一种情况下，维护必须安排在固定的位置(相对于作业顺序)。第二种考虑维修调度的情形，其中恶化只取决于作业的数量。第三种模型允许可变的维护持续时间，可以更灵活地控制机器的状态。这些非常基本的模型将在项目过程中进一步开发，以便它们能够更好地反映现实生活情况。为此，我们将结合不同模型的特点，分析允许抢占作业的情况，并根据机器的状态(例如，学习效果、恶化)引入处理时间。在最后阶段，我们将考虑多维机器的状态，这当然是最能反映现实生活情况的阶段。这里，每个状态维度可以是不同类型的，例如经典的依赖于时间的状态、作业数量或燃料水平。

Machine deterioration and preventive and predictive maintenance operation have been considered in the scheduling literature for quite a while. Most models assume that machine deterioration is time dependent in the sense that a machine deteriorates by age or by the time being in use. Moreover, a maintenance operation is classically assumed to be of a fixed duration, leading to a full recovery of the machine. These models neglect the fact that a machine’s deterioration may depend on factors such as the number of setups for a job or, more generally, can be expressed by a machine’s state, which might be influenced by each job individually. For example, in aviation, an aircraft’s state can be defined by flying hours, flying distance, and the number of flights. In preliminary work, the applicants developed three basic models. In the first one, maintenance has to be scheduled at fixed positions (with respect to the job sequence). The second considers a situation with maintenance scheduling in which the deterioration only depends on the number of jobs. The third model allows for variable maintenance duration, giving more flexible control over a machine’s state. These very basic models will be further developed in the course of the project so that they can better reflect real life situations. To do so, we will combine characteristics of the different models, analyze situations in which preemption of jobs is allowed, and introduce processing times depending on the machine’s state (e.g. learning effects, deterioration). In a final stage, which certainly reflects real life situations best, we will consider multidimensional machine’s states. Here, each state dimension might be of a different type, e.g. a classical time dependent state, the number of jobs, or a fuel level.