The construction sector is currently undergoing a shift from stick-built construction techniques to modular building systems. If construction supply chains are to support this transformation, they need to be modified and strengthened using an adapted logistics system. The aim of this study is to establish a mathematical model for the logistics of modular construction covering the three common tiers of operations: manufacturing, storage and construction. 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 be adapted to variations in demand on the construction site. We propose a Mixed Integer Linear Programming model that captures construction scenarios with demands for modular products that are either foreseeable or abruptly disrupted. The use of the model is illustrated through a case study of bathroom pods for a building project. The model outputs include supply chain configurations that reduce total costs across a range of scenarios. The model could serve as a decision support tool for modular construction logistics.