The replacement problem: A polyhedral and complexity analysis. The complete version
Preprint, 2009

We consider an optimization model for determining optimal opportunistic maintenance (that is, component replacement) schedules when data is deterministic. This problem, which generalizes that of Dickman et al., is a natural starting point for the modelling of replacement schedules when component lives are non-deterministic, whence a mathematical study of the model is of large interest. We show that the convex hull of the set of feasible replacement schedules is full-dimensional, and that all the necessary inequalities are facet-inducing. Additional facets are then provided through Chvatal-Gomory rounding. We show that when maintenance occasions are fixed, the remaining problem reduces to a linear program; in some cases the latter is solvable through a greedy procedure. We further show that this basic replacement problem is NP-hard.

opportunistic maintenance

replacement problem

mixed binary linear programming

polyhedral analysis

complexity analysis


Niclas Andréasson

Michael Patriksson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Ann-Brith Strömberg

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Adam Wojciechowski

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet




Grundläggande vetenskaper

Preprint - Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University