Maritime crude oil transportation problem have been drawing the attention of researchers for quite a long time. The cost incurred in the supply chain for the oil products is one of the biggest driving factors for these researchers. In the present paper, we have addressed the problem faced by the logistics section of the petroleum downstream industry. This industry mainly deals with the transportation of finished oil products like fuel oil, high speed diesel, etc. from refineries to the demand points. For this purpose, we have developed a mathematical model to represent the problem appropriately, aiming at total cost minimisation as well as service-level maximisation. The problem in hand is then tackled with a modified Multi-objective Ant Colony optimisation algorithm which besides considering more than one pheromone structure also involves non-dominated sorting of the results to give us the best-performing solution fronts. For the purpose of dealing with the uncertainties causing docking problems at a port, we have incorporated a second stage of route allocation for the vessels. Towards the end, we have carried out a sensitivity analysis for the parameters of the ant colony algorithm to get the combination of parameters for which this new type of algorithm performs best. The comparison of obtained results with one of the other contemporary algorithms also establishes the superiority of our heuristic.