Using and extending fix-and-relax to solve maritime inventory routing problems

The paper presents a new way of optimising maritime inventory routing problems (IRP) by using a heuristic approach based on fix-and-relax time decomposition extended with two new features. The purpose of the extensions is to reduce computation time during the fix-and-relax process and to improve solution quality after a first solution is found. The feature which improves solution quality is independent of the method used for calculating the first solution. In this study, the algorithm and extensions have been tested on four liquefied natural gas (LNG) cases and the impacts on computational time and objective function value are reported. The results show that using fix-and-relax reduces computing time considerably while the objective function value is only slightly worse compared to a general MILP solver. Furthermore, the results confirm that the extensions work according to the intentions when compared to the original fix-and-relax heuristic. For relatively complex cases, it appears advantageous to use the extensions developed.