The weighted uncapacitated planned maintenance problem: Complexity and polyhedral properties

This paper introduces the Weighted Uncapacitated Planned Maintenance Problem (WUPMP). Based on guaranteed maximum service intervals, the WUPMP pursues the finding of a maintenance schedule that minimizes the resulting total fixed and variable costs. One finding is that significant polyhedral attributes of its solution space are derived. Among them, quasi-integrality that allows for applying an integral simplex algorithm is proven. Moreover, we prove strong NP-hardness and propose an exact solution procedure that is polynomial if the number of considered maintenance activities or the number of periods is constant. Since at least one restriction applies to most real-world applications, the algorithm provides practical decision support. Furthermore, the complexity status of various polynomial special cases of the WUPMP is resolved.