At depots with refined oil shortage, arranging a reasonable distribution scheme with limited supply affects operation costs, demand satisfaction rate of gasoline stations (hereafter, ‘station satisfaction’), and overtime penalty. This study considers the refined oil distribution problem with shortages using a multi-objective optimisation approach from the perspective of decision makers of oil marketing companies. The modelling and solving process involves (i) formulation of a crisp multi-depot vehicle routing model with limited supply (MDVRPLS) which considers station priority and soft time windows, (ii) development of a robust optimisation model (ROM) to manage uncertainty in demand, and (iii) the proposal of a multi-objective particle swarm optimisation (MOPSO)algorithm. Results of numerical experiments show that (i) the crisp model can better balance operation costs, station satisfaction, and overtime penalty, which produces 3.33% and 4.60% increase in station satisfaction at an increased unit cost and overtime penalty respectively; (ii) ROM successfully addresses uncertainty in demand compared to the crisp model, which requires an additional 8.81% in cost and 12.85% in penalty; and (iii) the MOPSO manages these MDVRPLS models more effectively than other heuristic algorithms. Therefore, applying ROM of refined oil supply shortage to the management significantly improves the efficiency and resists the disturbance caused by external uncertainties, providing scope for efficient distribution of scarce resources.