# Resilient Scheduling as a Response to Uncertainty in Construction Projects
## 3 Application of Resilient Scheduling on a Test Problem Instance
### Validating Resilient Scheduling Process  
To validate the resilience of the proposed scheduling process, a probabilistic simulation analysis was conducted for different baseline solutions of the previously presented test problem. Due to the computational complexity of the underlying scheduling problem, the simulation analysis was bounded on two distinctive instances. The first baseline schedule refers to the single makespan instance obtained by solving the MOO test problem as previously described, while the other solution is found when the second and the third objective function were shifted in their hierarchy. For the second case, timeline minimization is still on the highest level of hierarchy in the optimization process; however, the profit maximization is in the second place of importance, and the surrogate measure maximization is at the bottom considering the hierarchical importance of objective functions. This way, the evaluation is made to compare the simulated behavior of two different baseline schedules: both of them have a duration of globally optimal 18 months, but in the first case, the SM value is higher and the baseline profit value is lower compared to SM value and baseline profit value from the second case. Objective function values for both cases are given in Table 7, along with the baseline start times for all activities, including dummy start and dummy end. The credit limit was set to 280 thousand of financial units in both cases. Since the goal of the simulation process is to analyse the project behavior under the impact of uncertainty, some of the activities' durations in the process of validation are allowed to take stochastic values. For this reason, the duration of activities 2, 4, and 6 in the project network are allowed to take stochastic values. Uncertain activity times are modeled with beta distribution, where shape parameters are set to \(\alpha=2\) and \(\beta=5\) in order to calculate realised activity durations in the Monte Carlo analysis. Stochastic activity durations in the simulation process are bounded between 0.7 and 2.2 of their estimated length, while the mode of the simulated activities is equal to the planned duration, \(d_{i}\). Considering the simulated direct cost for each activity, it is assumed that the new cost is proportionally related to the realized duration of activity at a ratio, R, which is used to delineate if the cost of activity (C\({}_{\text{a}}\)) at a simulated duration (T\({}_{\text{a}}\)) consists mainly of material or equipment and labour. For example, if the cost of activity consists mainly of material, it will have a lower ratio value, R, while higher dependence on equipment and labour will be represented with a higher R-value [70]. In the simulation analysis, R is set to 0.6 for all activities. To calculate activities' cost C\({}_{\text{a}}\) at a simulated duration T\({}_{\text{a}}\), Equation (14) is employed from the Reference [70]:  
\[\text{C}_{\text{a}}=\text{C}_{\text{m}}+\frac{(\text{T}_{\text{a}}-\text{T}_ {\text{m}})}{\text{T}_{\text{m}}}\times\text{R}\ \times\text{C}_{\text{m}}\;, \tag{14}\]  
where C\({}_{\text{m}}\) represents the original cost of activity at the deterministic duration, T\({}_{\text{m}}\). In the simulation analysis, additional resource relations are appended to accompany existing precedence connections between activities, so the baseline resource flow can be preserved throughout the entire simulation process. This way, resource conflicts are avoided through the simulation process where activities' durations take stochastic values. Additional resource relations are shown for each baseline schedule in Figure 4. Finally, the enhanced Monte Carlo simulation approach, which takes into consideration resource constraints, is taken on 10,000 iterations for each baseline case.