Dual heuristics and new dual bounds to schedule the maintenances of nuclear power plants

TL;DR

This paper develops dual heuristics and relaxations to compute high-quality dual bounds for scheduling maintenance of nuclear power plants, significantly improving previous bounds and providing insights for better solutions.

Contribution

It introduces new MIP relaxations and reduction techniques that enhance dual bounds for complex nuclear maintenance scheduling problems.

Findings

New dual bounds outperform previous literature

Reductions in time steps and scenarios guarantee bounds for the entire problem

Enhanced understanding of the problem structure and solution approaches

Abstract

The EURO/ROADEF 2010 Challenge aimed to schedule the maintenance and refueling operations of French nuclear power plants, ranking the approaches in competition for the quality of primal solutions. This paper justifies the high quality of the best solutions computing dual bounds with dual heuristics. A first step designs several Mixed Integer Programming (MIP) relaxations with different compromises between computation time and quality of dual bounds. To deal with smaller MIPs, we prove how reductions in the number of time steps and scenarios can guarantee dual bounds for the whole problem of the Challenge. Several sets of dual bounds are computable, improving significantly the former best dual bounds of the literature. Intermediate results allow also a better understanding of the problem and offer perspectives to improve some approaches of the Challenge.