# Two-Stage Stochastic Programming for Precast Module Water Transportation: A Case Study in Hong Kong
## 2 Literature Review  
Off-site construction relies on prefabricated products, which can accelerate the construction process, address declining productivity in the construction industry, and promote sustainable development. There are three levels of prefabricated products in off-site construction, ranging from the simplest form, prefabricated components (PCs), to the most complex form, MiC modules [13; 14]. PCs encompass structural elements such as beams, columns, and slabs, constructed from materials like reinforced concrete, steel, and wood. Key structural parts, including walls, floors, and roofs, are manufactured in factories as prefabricated panels, which offer a higher degree of standardization compared to individual components like walls [15]. These panels are then transported to the construction site for assembly, thereby streamlining the building process by shortening the overall timeline and minimizing on-site labor requirements. Modular integrated Construction (MiC) represents the pinnacle of off-site prefabrication, where entire sections of a building--such as hotel rooms or classrooms--are fully assembled in a factory setting before being delivered to the site [16]. While MiC can significantly improve construction productivity, its cost remains a critical factor influencing its widespread adoption. The cost of MiC is impacted by various factors, which need to be carefully considered to ensure its economic feasibility. The high initial cost, construction methods, size of the units, transportation of modules, and lack of government support may pose significant challenges if not properly addressed. [PERSON] and [PERSON] investigated automated assembly in MiC, focusing on how automation impacts time efficiency and cost [17]. [PERSON] et al. [18] developed a control system implemented in a structural steel prefabrication facility, minimizing the cost of MiC. Meanwhile, transportation costs for prefabricated products are among the top three contributors to the overall cost of MiC projects [19]. Assembling prefabricated products often leads to critical errors that are only discovered during on-site assembly, resulting in additional costs. These unforeseen expenses can significantly impact the overall budget and timeline of construction projects, highlighting the importance of meticulous planning and quality control in the prefabrication process [20]. In module production, various uncertainties decrease the effectiveness of production planning, scheduling, and execution, increasing construction periods and costs [21]. The transportation of prefabricated products, which ranges in complexities from individual components (e.g., precast columns) to MiC modules, plays an important role in off-site construction. Inefficient transportation of prefabricated products may lead to economic losses as well as difficulties in storage or construction progress [22; 23]. To avoid these, the transportation plan of prefabricated products needs to be well designed [24]. Many previous studies have attempted to solve the transportation planning problems for prefabricated products. Table 1 classifies them based on various criteria, including the transportation modes, prefabrication level, optimization model, solution method, optimization objective, and whether they considered the uncertainty.