The traditional in-situ construction method is currently being replaced by modular building systems, that take advantage of modern manufacturing, transportation, and assembly methods. This transformation poses a challenge to construction supply chains, which have, thus far, been concentrated on raw material transportation only. A mathematical model is conceived in this study for the design and optimisation of risk-averse logistics configurations for modular construction projects under operational uncertainty. The model considers the manufacturing, storage, and assembly stages, along with the selection of optimal warehouse locations. Using robust optimisation, the model accounts for common causes of schedule deviations in construction sites, including inclement weather, late deliveries, labour productivity fluctuations and crane malfunctions. A school dormitory construction project is used as a case study, demonstrating that the proposed model outperforms existing techniques in settings with multiple sources of uncertainty.