# Two-Stage Stochastic Programming for Precast Module Water Transportation: A Case Study in Hong Kong
## 2 Literature Review
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Study**} & **Transportation** & **Prefabrication** & **Whether Use** & **Optimization Objective(s)** & **Consideration of** \\  & **Mode** & **Level** & **Optimization** & & **Uncertainty** \\ \hline
[25] & Road & PC & Yes (Heuristic algorithm) &
\begin{tabular}{c} Minimize the transportation \\ process time and the penalties \\ \end{tabular} & \(\times\) \\
[26; 27] & Road & PC & Yes (Heuristic algorithm) & Minimize the transportation cost & \(\times\) \\
[28] & Road & PC & Yes (Heuristic algorithm) & Minimize the carbon emissions & \(\times\) \\
[29] & Road & PC & Yes (Heuristic algorithm) & Minimize the total logistics cost & \(\times\) \\
[30] & Road & PC & Yes (Heuristic algorithm) & Minimize the total logistics cost & \(\surd\) \\
[31] & Road & PC & Yes (Heuristic algorithm) &
\begin{tabular}{c} Maximize the degree of \\ completion of transportation \\ \end{tabular} & \(\surd\) \\
[32] & Road & PC & Yes (Heuristic algorithm) & Minimize the transportation cost & \(\surd\) \\
[24] & Road & PC & Yes (Exact method based & Minimize the transportation cost & \(\surd\) \\
[10] & Road & MiC & Yes (Heuristic algorithm) & Minimize the truck loss time & \(\times\) \\
[33] & Road & MiC & No (Multi-agent & Minimize the transportation cost & \(\times\) \\
[34] & Road & MiC & Yes (Heuristic algorithm) & Minimize the total logistics cost & \(\times\) \\
[35] & Road & MiC & Yes (Exact method based & Minimize the transportation cost & \(\times\) \\
[36] & Road & MiC & Yes (Exact method based & Minimize the total logistics cost & \(\times\) \\
[13] & Road & MiC & Yes (Exact method based & Minimize the total logistics cost & \(\surd\) \\
[37; 38] & Water & PC & Yes (Heuristic algorithm) & Minimize the transportation cost & \(\times\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of studies on transportation planning in off-site construction. As shown in Table 1, various mathematical programming techniques (e.g., linear programming, nonlinear programming, integer programming, and mixed-integer programming) were employed in previous research to model the transportation planning problem of prefabricated products. Cost is a dominant factor considered by contractors [19; 41], and transportation cost is consistently identified as one of the top three contributors to total costs [42]. The optimization objectives were mainly concerned with minimizing the total logistics cost (including the storage and transportation costs) or just transportation costs in the literature. Undeniably, prefabricated products can be stored at sites for in-time delivery when space permits [32; 43], but high-density cities like Hong Kong lack available space for the temporary storage of MiC modules before installation [44]. Additionally, storage incurs extra costs that can burden the implementation of MiC projects. Therefore, integrating just-in-time (JIT) manner into module transport planning is essential [45]. [PERSON] et al. [25] proposed a genetic algorithm to efficiently manage the transportation of prefabricated components. Similarly, [PERSON] et al. [28] and [PERSON] et al. [30] employed the identical algorithmic approach, albeit with distinct optimization targets. The former focused on mitigating carbon emissions arising from transportation, while the latter concentrated on minimizing the total logistics costs. The particle swarm optimization algorithm was applied to resolve a scheduling model in the transportation phase [26] and optimize the dynamic transportation of prefabricated components [32]. [PERSON] et al. [27] implemented an enhanced hybrid difference firefly algorithm to solve the planning of vehicles from off-site factories to construction sites. A scheduling planning algorithm for the optimization of truck loss time was proposed under the constraints of construction demand for prefabricated components [10]. [PERSON] et al.