Efficient transportation planning is essential for improving supply chain performance, particularly in multi-stage networks where transport mode and route selection significantly affect total logistics cost. This study develops a Linear Programming (LP) model to minimize fixed transportation costs across a three-stage multimodal supply chain of a paper mill in Bangladesh. Using real data on supply, demand, and fixed route costs, the model optimizes shipment allocation from suppliers to the factory, from the factory to distribution centers, and from distribution centers to retailers using road, rail, or a combined mode. Results indicate that while rail transport offers lower unit costs, limited rail connectivity prevents full demand fulfillment; in contrast, the combined mode selecting the lowest-cost option per route satisfies all demand and reduces total fixed transportation cost by 18.4% compared to road-only transport. Overall, the findings demonstrate that integrating road and rail transport significantly improves cost efficiency in developing-country logistics networks and provides a practical, easily implementable framework for optimizing fixed-cost transportation decisions in the paper mill supply chain