## 4 Model Development
### DP Procedure  
The multifaceted nature of construction management is manifested in an array of interdependent tasks, strict resource allocations, and bounded deadlines set against overarching budget constraints. It is not merely a logistical venture but a computational conundrum where numerous variables, such as material procurement, manpower deployment, machinery scheduling, and potential environmental variables, intertwine. To address these issues, an algorithm having an appropriate form for the problem structure is needed. DP is an algorithmic technique used to solve complex problems by breaking them down into smaller subproblems. A particular problem is divided into smaller subproblems, with their solution values stored to avoid redundant calculations, ultimately facilitating the derivation of a final solution. In the context of this research, the desired model development required an algorithm that could produce solutions decisively, ensuring rapid and accurate results rather than relying on highly complex optimization algorithms. Therefore, a scheduling model for detailed earthwork in road construction at the planning stage was developed using the DP method. The DP algorithm starts by considering various processes, each comprising different tasks. Every task within a process has an assigned cost and duration. Some of these processes can operate simultaneously, and there is a specified deadline. To facilitate the algorithm, a DP table is constructed, determined by the deadline and the number of processes. This DP table's main purpose is to identify the smallest possible cost to meet the deadline for every process. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Main** & **Middle** & **Subcategory** & **Detailed** & **Standard Daily Workload (m\({}^{3}\))** & **Cost** \\
**Category** & **Category** & **Condition** & **Condition** & **(W)** \\ \hline \multirow{6}{*}{} & \multirow{6}{*}{breaking} & & 36.80 & 986,583 \\  & & & 26.40 & 826,535 \\  & & concrete pavement & & 14.00 & 751,759 \\  & & T \textless{} 30 cm & 128.00 & 986,583 \\  & & T \textless{} 20 cm & 55.20 & 826,535 \\  & & pavement & T \textless{} 20 cm & 32.80 & 751,759 \\  & & T \textgreater{} 30 cm & 100.00 & 986,583 \\  & & removing sidewalk & & 360.00 & 1,406,713 \\  & & block packaging & & 600.00 & 1,367,731 \\  & & concrete cutting & & 450.00 & 1,028,981 \\  & & asphalt cutting & & 500.00 & 1,028,981 \\  & & removing & & 166.67 & 2,572,898 \\  & & revement block & & 126.98 & 1,121,664 \\  & & removing & mattress form wire & 320.00 & 4,495,991 \\  & & cylinder & & \\  & & removing & column spacing & 210.00 & 3,344,739 \\  & & 2 m & & 140.00 & 2,428,951 \\  & & & 70.00 & 1,547,874 \\  & & column spacing & & 420.00 & 3,511,913 \\  & & & 280.00 & 2,642,837 \\  & & & 140.00 & 2,021,185 \\  & & bridge guardrail & & 171.31 & 1,262,600 \\  & & demolition & & 342.56 & 1,535,571 \\  & & & 513.84 & 2,159,685 \\  & & crushing & & 668.54 & 13,313,202 \\ construction waste & & & 668.54 & 6,659,765 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._During the implementation phase, the algorithm examines each time unit for every process, from the onset to the given deadline. For processes that operate independently, the algorithm evaluates their tasks. It then updates the table by adding the cost of the task to the time previously used and subtracts the duration of the task. Conversely, for processes that can run concurrently with others, the algorithm assesses tasks from all simultaneous processes. The table is then adjusted by considering the total task costs and subtracting the duration of the task that takes the longest. This methodology is particularly relevant in the context of construction projects. Large construction projects often involve multiple phases, each with its unique challenges and variables. DP provides a systematic mechanism for identifying each phase, thus examining it individually and determining a cost-effective strategy tailored to it.