The Sum Colouring Problem is an NP-hard problem derived from the well-known graph colouring problem. It consists in finding a proper colouring which minimizes the sum of the assigned colours rather than the number of those colours. This problem often arises in scheduling and resource allocation. In this paper, we conduct an in-depth evaluation of ILP and CP's capabilities to solve this problem, with several improvements. Moreover, we propose to combine ILP and CP in a tree decomposition with a bounded height. Finally, those methods are combined in a portfolio approach to take advantage from their complementarity.