The construction sector is currently undergoing a shift from stick-built construction to modular building systems that take advantage of modern prefabrication techniques. Long established in-situ construction practices are thus being replaced by processes imported from the manufacturing sector, where component fabrication takes place within a factory environment. As a result of this transformation, current construction supply chains, which have focused on the delivery of raw materials to sites, are no longer apt and need to make way to new, strengthened, and time-critical logistics systems. The aim of this study is to establish a mathematical model for the optimisation of logistics processes in modular construction covering three tiers of operation: manufacturing, storage and assembly. Previous studies have indicated that construction site delays constitute the largest cause of schedule deviations. Using the model outlined in this paper we seek to determine how factory manufacturing and inventory management should react to variations in the demand on construction sites. A two-stage stochastic programming model is developed to capture all possible demand variations on site. The model is evaluated using a case study from the residential construction sector. The application shows that the model is effective and can serve as decision support to optimise modular construction logistics.