# Two-Stage Stochastic Programming for Precast Module Water Transportation: A Case Study in Hong Kong
## 1 Introduction  
Modular integrated Construction (MiC) constitutes a transformative construction approach where free-standing modules with internal finishes, fixtures, and fittings are prefabricated at off-site factories, and subsequently transported for assembly at construction sites [1, 2]. The prefabrication of MiC modules significantly shortens construction timelines and enhances health and safety conditions at construction sites [3]. However, the off-site production of MiC modules introduces new challenges to transportation planning. MiC projects cost a premium ranging from 15% to 20% compared to traditional construction methods, mainly due to the high transportation cost [4, 5], hence, hampering the broader adoption of MiC [6, 7]. The transportation of modules primarily involves two modes: road and water transportation. Road transportation is widely favored for its flexibility, offering door-to-door delivery directly to construction sites and eliminating the need to transfer modules between different transport modes. However, road transportation is characterized by high costs per individual module, rendering it economically inefficient for long distances and large-scale MiC projects. For instance, in Hong Kong, road transportation expenses comprise approximately 30% of total MiC project costs [8]. Compared to road transportation, water transportation provides a more cost-effective option for the multimodal long-distancetransport of large volumes of modules in certain regions (e.g., Hong Kong) [8]. Despite the advantage, water transportation necessitates meticulous coordination. Shipping schedules are generally predetermined, requiring planners to reserve barge capacities in advance based on their expected module demand. This characteristic adds complexity to the logistics of transporting modules via water. Although water transportation is recognized as a more economical and suitable mode for large-scale MiC projects [9], the intricacies involved in the transport planning of MiC modules via water remain relatively underexplored [8]. Uncertain module demand is identified as a key challenge in water transport planning for modules [10]. The demand is highly subjective to factors, such as weather conditions, equipment breakdown, and workers' expertise [11], which greatly impact module water transportation. This is because the adoption of water transportation requires planners to make booking decisions based on an estimated module demand, but the actual demand is only realized in later stages. If the capacities of the booked barges are unable to cater to the actual demand for modules at the construction site, transport planners would have to temporarily rent barges at higher rates to transport the surpluses to avoid project delay. Eventually, this leads to high additional module transportation costs. In contrast, if the capacities of the booked barges exceed the actual module demand, the transport planner is still liable for the costs of the wasted barge capacities. Consequently, it is crucial to consider the uncertain demand when making the water transportation plan for MiC projects. However, existing optimization methods of transportation planning employed in previous research often overlook the uncertainty in module demand, hence, potentially limiting their practical applicability in real-world scenarios [12]. This study sets forth to achieve three primary objectives: (1) to design a stochastic module water transport planning framework considering the uncertainty of weekly module demand; (2) to validate the effectiveness of the proposed stochastic model using real Hong Kong data; and (3) to identify the influence of barge rental on the total transportation costs through sensitivity analyses. This study offers a novel transportation planning model that not only minimizes transportation costs but also accounts for the inherent uncertainty in module demand in MiC projects.