The liner shipping fleet repositioning problem (LSFRP) is a central optimization problem within the container shipping industry. Several approaches exist for solving this problem using exact and heuristic techniques, however all of them use a single objective function for determining an optimal solution. We propose a multi-objective approach based on a simulated annealing heuristic so that repositioning coordinators can better balance profit making with cost-savings and environmental sustainability. As the first multi-objective approach in the area of liner shipping routing, we show that giving more options to decision makers need not be costly. Indeed, our approach requires no extra runtime than a weighted objective heuristic and provides a rich set of solutions along the Pareto front.