State Dependent Maintenance Scheduling

机器退化和预防性和预测性维护操作已被认为是在调度文献相当长的一段时间。大多数模型假设机器的劣化是时间依赖的，在某种意义上说，机器的劣化是由年龄或使用时间引起的。此外，传统上假定维护操作具有固定的持续时间，从而导致机器的完全恢复。这些模型忽略了这样一个事实，即机器的劣化可能取决于诸如作业的设置次数等因素，或者更一般地说，可以由机器的状态来表示，这可能会受到每个作业的单独影响。例如，在航空中，飞机的状态可以由飞行小时、飞行距离和飞行次数来定义。在初步工作中，申请人开发了三个基本模型。在第一种情况下，必须在固定位置（相对于作业顺序）安排维护。第二个考虑的情况下，维修调度的恶化只取决于工作的数量。第三种模型允许可变的维护持续时间，从而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得到进一步发展，以便更好地反映真实的生活情况。为此，我们将结合不同模型的联合收割机特性，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。在最后一个阶段，当然最能反映真实的生活情况，我们将考虑多维机器的状态。这里，每个状态维度可以是不同的类型，例如经典的时间相关状态、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.