State Dependent Maintenance Scheduling

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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.