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By leveraging advanced techniques and models, Operations Research (OR) provides critical insights and strategic interventions across multiple domains, including transportation, communication, project management, and supply chain optimization. The field's multifaceted approach continues to drive efficiency and innovation in numerous industries. This paper thoroughly evaluates numerous approaches and methods researchers employ to model and investigate problems. Our objective is to bridge gaps in existing literature by examining recent advancements in this field. Network flow problems encompass the shortest path, maximal cost flow, and minimal cost flow problems. These critical elements are essential for understanding transportation dynamics, communication, and resource allocation networks. Furthermore, we explore real-life scenarios where these network flow problems arise, shedding light on their practical significance.