We propose a constraint programming approach for the optimization of inventory routing in the liquefied natural gas industry. We present two constraint programming models that rely on a disjunctive scheduling representation of the problem. We also propose an iterative search heuristic to generate good feasible solutions for these models. Computational results on a set of large scale test instances demonstrate that our approach can find better solutions than existing approaches based on mixed integer programming, while being 4 to 10 times faster on average.