Because of the fission process that consumes the fuels, the old fuel rods must be replaced periodically with fresh ones (this is called a (replacement) cycle). During a given replacement cycle only some of the assemblies (typically one-third) are replaced since fuel depletion occurs at different rates at different places within the reactor core. Furthermore, for efficiency reasons, it is not a good policy to put the new assemblies exactly at the location of the removed ones. Even bundles of the same age will have different burn-up levels due to their previous positions in the core. Thus the available bundles must be arranged in such a way that the yield is maximized, while safety limitations and operational constraints are satisfied. Consequently, reactor operators are faced with the so-called optimal fuel reloading problem, which consists of optimizing the rearrangement of all the assemblies, the old and fresh ones, while still maximizing the reactivity of the reactor core so as to maximise fuel burn-up and minimise fuel-cycle costs.