This study delves into the complexities of a multi-objective minimal cost flow (MMCF) problem, focusing on the intricacies of transporting a variety of commodities from multiple sources to their intended destinations. The investigation recognizes the presence of several transportation alternatives, each with its distinctive capacity constraints tailored to the specific requirements of each commodity being moved. In addressing this transportation and distribution challenge, the study acknowledges that the resulting model may not inherently achieve a state of balance between the supply and demand across the network. To tackle this issue, a novel method is proposed that effectively solves the MMCF problem directly, circumventing the need for balance by not requiring the model's conversion to a balanced state. Furthermore, the research offers a thorough discussion on the advantages of the proposed solution method. These benefits are dissected in terms of efficiency, cost-effectiveness, and scalability, providing valuable insights into their applicability for complex logistical operations. The method's potential for adaptability in various operational contexts is also scrutinized, demonstrating its versatility in managing the multi-faceted dimensions of multi-commodity flow problems. By not adhering to the traditional balanced model requirement, the study breaks new ground, proposing an approach that could potentially streamline operations and lead to more sophisticated models and algorithms in the field of multi-objective optimization. The research opens avenues for further exploration into cost-efficient, capacity-conscious transport strategies that could redefine logistical practices.