Complex linear infrastructure projects have a unique characteristic that the construction site moves as the project progresses, necessitating that off-site manufacturing should be mobile. A mobile prefabrication factory is a promising distributed production facility that meets such requirements and offers benefits such as carbon emissions reduction by shortening the distance between the construction site and the off-site prefabrication facility. However, factory relocations introduce significant variability in the distances for transporting materials to the factory and delivering the completed prefabricated elements from the factory to the construction site. This paper presents an integer linear programming model to identify a feasible relocation strategy that reduces the overall transportation carbon emissions. A case study of hyperloop construction, an ultra-high-speed vacuum ground transportation infrastructure, is conducted as a demonstration. The results show that using mobile prefabrication factories to supply linear infrastructure projects can significantly reduce the overall transportation carbon emissions by around 50% compared to the fixed factory scenario. The primary factor to optimize this problem is the total transportation distance of the prefabricated elements. Relocating the mobile factory four to six times aligns with achieving efficient performance in terms of reducing carbon emissions. This analysis offers insights into developing feasible factory relocation strategies for decision-makers in complex linear infrastructure projects.