# Multi-Objective Resource-Constrained Scheduling in Large and Repetitive Construction Projects
## 4 Case Study  
The case study includes a 160-activity project which consists of 16 repetitive identical basic projects of 10 activities each. The whole project is formed by considering four basic projects in a serial execution form, which are then scaled up in a parallel quadruple execution arrangement, as shown in Figure 2. The resulting project can be considered a typical repetitive and large project. The input data of the basic 10-activity project are shown in Table 2, while its network diagram is illustrated in Figure 3 ([38]). The project has been designed to include diverse features of a (construction) project (e.g., activities that can take place in parallel or be executed alone (in the case of task J), time floats of different sizes, etc.). The number of resources for all activities has been assumed at two units per day. Even though in practice, several types of resources are used in (construction) projects, in this case study, a single resource type is considered for all activities. In general, if there are two or more resource types, the effectiveness in resource allocation may be hindered by the conflicting requirements of different resource types of project activities. This means that a schedule that leads to a nice resource histogram of one resource type may not provide a desirable allocation of another resource type. As a result, the global solution may already present some resource allocation inefficiencies and, as such, the capability of the optimizer cannot be objectively assessed. Using a single resource type, the optimal resource pattern may be developed beforehand, especially in small projects. Therefore, the net outcome of the optimization can be assessed. Further, the solution space for a particular project is the same (it includes all feasible alternative schedules), irrespective of the number of resource types. Thus, the problem size remains the same with the exception that some additional calculations for the added resource types are required in each optimization step. Figure 2: Network diagram structure of the examined project. The activity durations and resources have been set in a way that facilitates the development of a perfectly flat resource histogram in certain cases of the following analyses, and this is the reason for assuming uniform resource usage in all activities. Prior knowledge of the exact solution is important in objectively evaluating the actual convergence potential of the optimization process. With the input data of the case study example, the minimum duration of the basic project is 17 days, while for the full project, it is 68 days. The resource allocation histogram of the project, in its default early start scheduling form, presents significant peaks and valleys in resource demand throughout the project length (Figure 4). The repetitive resource allocation pattern in the diagram results from the serial execution of sub-projects. The high resource demand at specific periods may be difficult to serve, while the high resource fluctuations at specific time points require expenditures for transferring resources in and out of the construction site. A typical optimization run develops a resource allocation plan, such as the one shown in Figure 5. The top part presents the resource requirements of the full project, while the following diagrams show the resource allocation of the series of sequential sub-projects. \begin{table}
\begin{tabular}{c c c c} \hline
**Activity** & **Predecessors** & **Duration** & **Resources** \\ \hline A & Start & 5 & 2 \\ B & Start & 10 & 2 \\ C & Start & 4 & 2 \\ D & A & 7 & 2 \\ E & C & 5 & 2 \\ F & A & 4 & 2 \\ G & B, D, E & 3 & 2 \\ H & C & 6 & 2 \\ I & Start & 4 & 2 \\ J & F, G, H, I & 2 & 2 \\ \hline \end{tabular}
\end{table} 
Table 2: Project data for the applied example. Figure 4: Resource histogram for the early start project schedule. Figure 3: Network diagram of the basic project. The different colors indicate the contribution of each basic project within the sequential structure.