Exact approaches for the orderly colored longest path problem: Performance comparison.

•We propose three new formulations for the Orderly Colored Longest Problem.•The performance of models is enhanced by introducing a priori cuts, valid inequalities and strengthen versions of the basic constraints.•The computational results show that one of the three models (CFF) outperforms the others both in terms of computational time and quality of the solutions.•CFF could be considered the reference for the optimal solution of Orderly Colored Longest Path Problems.