The Minimum Sum Colouring Problem is an N P-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. Mainly incomplete approaches were proposed, but Integer Linear Programming (ILP) and Constraint Programming (CP) have also been used. In this paper, we conduct a more in-depth evaluation of ILP and CP's capabilities to solve the sum colouring problem, with several improvements. Moreover, we propose to combine ILP and CP in a tree decomposition with a bounded height.