The replacement problem: A polyhedral and complexity analysis
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.

mixed binary linear programming

replacement problem

polyhedral analysis

opportunistic maintenance

complexity analysis

Författare

Niclas Andréasson

Michael Patriksson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Ann-Brith Strömberg

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Adam Wojciechowski

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Ämneskategorier

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

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