# Multi-Objective Resource-Constrained Scheduling in Large and Repetitive Construction Projects
## 4 Case Study
The red line in the cumulative diagram indicates the daily resource availability, which corresponds to the mean resource requirement and indicates the ideal scenario of a perfect resource allocation scheme. The diagrams reveal that diverse (non-repetitive) resource patterns are built for each sub-project independently from others in both directions of the project scaling-up. This observation indicates that the whole project is treated as a rather \"random\" structure. It is also shown that the sub-projects in each series do not interfere with each other, following the serial deployment setting and constraints. In terms of resource allocation effectiveness, a highly leveled resource diagram has been developed around the average of 16 resources per day for a 100-day duration. As stated above, the analysis considers alternative optimization criteria either individually or in combination. Initially, each decision criterion is optimized individually. This is conducted to explore the full performance potential of each criterion without any interference with other possible objectives. Next, optimization is performed with pairs of criteria, especially those that are not linked with a linear relation. Finally, two-step optimization is examined, based on distinct criteria, to explore any potential improvements. Alternate constraint levels for resource availability and project completion time are considered to provide a comprehensive assessment of the process output and effectiveness. Figure 5: Typical optimized resource allocation diagram. The red line indicates the daily resource availability. Figures 6-12 indicatively present the optimal resource allocation histograms associated with a project duration of 160 days to obtain a pictorial form of the solution quality. The red line in each diagram indicates the daily resource availability. It is observed that the decision criteria STD, RLE, and MaxR end up as quite leveled histograms as they attempt to spread out resources across the whole project makespan and in numbers that are close to the resource availability level (Figure 6, Figure 7, and Figure 8, respectively). Among them, the STD and RLE criteria provide comparable resource histograms (in terms of resource usage fluctuations) and appear to perform better than the MaxR criterion in lessening such fluctuations. In a different direction, the RIO criterion results in resource allocation patterns that avoid high day-by-day resource usage alterations. To minimize the cumulative deviation of such kind, the resulting schedule typically does not fill the whole project length availability (Figure 9). Inevitably, the cumulative resource units exceeding the preset resource availability threshold (i.e., RLE value) increase in comparison to the previous criteria. However, the resource allocation histogram presents fewer and smoother resource transitions from day to day. Figures 10 and 11 illustrate representative resource histograms when bi-objective optimization of two criteria is applied, namely STD or RLE with RIO, respectively. As expected, the obtained solutions lie somewhere in between those provided by the corresponding single-criterion considerations. The importance of this analysis lies in its capacity to consider conflicting criteria with their corresponding actual costs to provide a solution that minimizes the total cost. Finally, the potential effectiveness of a two-step sequential optimization process incorporating different criteria is examined. In this example, the RLE or the STD criterion is first employed, leading to the corresponding best possible solution. Starting from this solution, a second optimization is performed using the RIO criterion. Figure 12 provides an indicative output of the sequential optimization of the STD and RIO criterion. Further discussion of the results is provided next. Figure 11: Resource histogram for RLE-RIO criterion. The red line indicates the daily resource availability. Figure 8: Resource histogram for MaxR criterion. The red line indicates the daily resource availability.