# Emergency Repair Scheduling Model for Road Network Integrating Rescheduling Feature
## 4 Case Analysis and Discussion
### Responsibility Area  
The current practices in Taiwanese public sectors on emergency repair scheduling issues are based on the concept of responsibility area. The lines of responsibility in Figure 2 are used to delineate the emergency repair areas of different maintenance units. Case 1, dividing into three responsibility areas, and including three resource points and fifteen disaster points, is presented in Figure 2 to validate the proposed model and further analyze the optimized results. In Case 1, the equipment resources in this study are excavators and bulldozers, with R1 resource representing the excavators and R2 resource representing the bulldozers; their corresponding quantities at different resource points are shown in Table 2. Detailed information of the combinations of equipment resources required for each disaster point and the corresponding repair durations for each combination of resources is shown on Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Resource Point No.** & **R1 Quantity** & **R2 Quantity** \\ \hline
1 & 6 & 6 \\
2 & 3 & 3 \\
3 & 5 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Resource types and quantity (Case 1). Figure 2: Diagram of the responsibility areas of Case 1. The possible route is defined as a two-way traffic path, and if we take repair activity at 14 and 15 in Case 1 as an example, the transit activity between these two disaster points can be divided into (1) transit from disaster point 14 to disaster point 15 and (2) transit from disaster point 15 to disaster point 14. The definition of a repair activity in the RCPSP framework is that the repair activity always exists in a repair project, as it must be fully completed as part of a repair project. However, a transit activity exists in a repair project only when equipment resources are being transited to a disaster point via this route, otherwise it is only a possible route, and if it is not selected for resource transit, then such transit activity does not exist in the RCPSP environment, during solution seeking runtime. Information of each resource transit route, including departing location, arrival location, and route travel time, is shown in Table 4.  
From the optimized results of the proposed model, the whole emergency repair process is shown in Figure 3 and the scheduling results are shown in Table 5. The minimum total duration of this repair project in Case 1 is 147 (unit: 20 min). To summarize, new disaster points and new resources will definitely affect the original repair schedule, so the proposed model must integrate the feature of rescheduling. Accordingly, this study applies a rescheduling feature so that the model can reschedule all repair works after the occurrence of a new disaster or the addition of new resources. In order to verify that the proposed model can take into account the addition of new disaster and resource points, Case 2 is presented for further analysis. Case 2 analysis is divided into three parts, with the following scenarios: (1) the initial phase of the disaster, including one resource point and six disaster points; (2) a subsequent disaster occurs at \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Disaster Point No.**} & **R1 Required** & **R2 Required** & **Repair Duration** \\  & **Quantity** & **Quantity** & **(in 20 min)** \\ \hline
4 & 1 & 1 & 30 \\ \hline
5 & 3 & 3 & 45 \\  & 3 & 2 & 53 \\ \hline
6 & 4 & 3 & 18 \\  & 3 & 3 & 23 \\ \hline
7 & 2 & 2 & 72 \\  & 2 & 1 & 85 \\ \hline
8 & 2 & 1 & 19 \\  & 1 & 1 & 24 \\ \hline
9 & 1 & 1 & 53 \\ \hline
10 & 2 & 1 & 60 \\  & 1 & 1 & 72 \\ \hline
11 & 1 & 1 & 15 \\ \hline
12 & 2 & 2 & 31 \\  & 1 & 1 & 52 \\ \hline
13 & 2 & 2 & 17 \\  & 1 & 1 & 29 \\ \hline
14 & 2 & 1 & 12 \\  & 1 & 1 & 17 \\ \hline
15 & 1 & 1 & 12 \\ \hline
16 & 2 & 1 & 30 \\  & 1 & 1 & 35 \\ \hline
17 & 3 & 2 & 90 \\  & 2 & 2 & 103 \\ \hline
18 & 2 & 2 & 54 \\  & 1 & 1 & 92 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Resources required for disaster point and corresponding repair durations (Case 1).