The weighted Genome Sorting Problem (wGSP) is to find a minimum-weight sequence of rearrangement operations that transforms a given gene order into another given gene order using rearrangement operations that are associated with a predefined weight. This paper presents a polynomial sized Integer Linear Program -called GeRe-ILP- for solving the wGSP for the following three types of rearrangement operations: inversion , transposition, and inverse transposition. GeRe-ILP uses variables and constraints for gene orders of length . It is studied experimentally on simulated data how different weighting schemes influence the reconstructed scenarios. The influences of the length of the gene orders and of the size of the reconstructed scenarios on the runtime of GeRe-ILP are studied as well.