# Emergency Repair Scheduling Model for Road Network Integrating Rescheduling Feature
## 3 Methodology
### Model Formulation
\begin{table}
\begin{tabular}{c l} \hline \hline
**Parameter** & **Statement** \\ \hline \(d_{u}\) & Duration of repair activity \(u\) at disaster point \(u\) \\ \(lt_{nj}\) & Duration of transit activity \(\eta i\) from resource point \(n\) to succeeding disaster point \(j\) \\ \(lt_{ij}\) & Duration of transit activity \(ij\) from preceding disaster point \(i\) to succeeding disaster point \(j\) \\ \(lf_{i}\) & Latest finish time of repair activity \(i\) at disaster point \\ \(r_{n}^{k}\) & Resource supply quantity of resource type \(k\) at resource point \(n\) \\ \(r_{sn}^{k}\) & Resource supply quantity of resource type \(k\) at resource point \(n\) for responsibility area \(s\) \\ \(rl_{i}^{k}\) & Maximum resource quantity that resource type \(k\) can be accommodated at disaster site \(i\) \\ \hline
**Variable** & **Statement** \\ \hline \(T\) & Total project duration \\ \(T_{s}\) & Total duration of responsibility area \(s\) \\ \(S_{u}\) & Start time of repair activity \(u\) \\ \(F_{u}\) & Finish time of repair activity \(u\) \\ \(S_{i}\) & Start time of preceding repair activity \(i\) \\ \(F_{i}\) & Finish time of preceding repair activity \(i\) \\ \(F_{i}\) & Finish time of preceding repair activity \(i\) \\ \(F_{si}\) & Finish time of preceding repair activity \(i\) \\ \(S_{j}\) & Start time of succeeding repair activity \(j\) \\ \(S_{nj}\) & Start time of transit activity \(\eta i\) from resource point \(n\) to succeeding disaster point \(j\) \\ \(F_{nj}\) & Finish time of transit activity \(ij\) from preceding disaster point \(i\) to succeeding disaster point \(j\) \\ \(S_{ij}\) & Start time of transit activity \(ij\) from preceding disaster point \(i\) to succeeding disaster point \(j\) \\ \(F_{ij}\) & Finish time of transit activity \(ij\) from preceding disaster point \(i\) to succeeding disaster point \(j\) \\ \(R_{i}^{k}\) & Resource usage of resource type \(k\) of preceding repair activity \(i\) \\ \(R_{j}^{k}\) & Resource usage of resource type \(k\) of succeeding repair activity \(i\) \\ \(RN_{i}^{k}\) & Remaining resource quantity after resource type \(k\) deployment for repair activity \(i\) \\ \(LR_{nj}^{k}\) & Resource quantity of resource type \(k\) dispatched through transit activity \(\eta i\) from resource point \(n\) to succeeding \\ \(LR_{nj}^{k}\) & Resource quantity of resource type \(k\) dispatched through transit activity \(ij\) from preceding disaster point \(i\) to succeeding disaster point \(j\) \\ \(LT_{nj}\) & Duration of transit activity \(nj\) from resource point \(n\) to succeeding disaster point \(j\) \\ \(LT_{ij}^{l}\) & Duration of transit activity \(ij\) from preceding disaster point \(i\) to succeeding disaster point \(j\) \\ \hline
**Set** & **Statement** \\ \hline \(S\) & Set of emergency repair projects \\ \(SS_{f}\) & Set of responsibility areas, where \(f=1,2,3,\,\ldots,\,g\) \\ \(SN\) & Set of resource points \\ \(SU\) & Set of recovery activities \\ \(SI\) & Set of preceding repair activities \\ \(SJ\) & Set of succeeding repair activities \\ \(SK\) & Set of resource types \\ \(SE_{t}\) & Set of in-progress repair activities at time interval \(t\), where \(t=1,2,3,\,\ldots,\,T\) \\ \(D_{u}\) & Set of the corresponding durations to different resource combinations for repair activity \(u\) \\ \(D_{nj}\) & Set of durations of transit activity \(nj\) from resource point \(n\) to succeeding disaster point \(j\) \\ \(D_{ij}\) & Set of durations of transit activity \(ij\) from preceding disaster point \(i\) to succeeding disaster point \(j\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters and variables of the proposed model.