In this work, we consider a multi-objective minimal cost flow (MMCF) problem where there are several commodities to transport from sources to destinations and there is more than one conveyance for those transporting. We also assume that in each conveyance, there are distinct capacities for each commodity. The obtained model is not necessary balanced, and we introduced a method to solve this model without converting it to a balanced model. Some advantages of the proposed method is discussed.