# Optimizing Ambulance Allocation in Dynamic Urban Environments: A Historic Data-Driven Approach
## 5 Conclusions  
In this study, we defined the multi-period ambulance relocation problem based on a mathematical programming model and derived its solution. We organized the analysis area into subzones in the form of hexagonal cells. Then, we mapped the demand in each cell based on historical ambulance call data. The organized data were the input to our proposed mathematical model. Through analyzing a solution of the proposed model, we observed that the demand was covered by about 1.33% more, and the number of zero zones, where it is difficult for an ambulance to reach in the golden time, was reduced by 47.37%. We also observed that the ambulances were redeployed appropriately to meet the changes in demand at each time point. Furthermore, we showed that the mathematical model presented in the case study can efficiently improve the number of zero zones even with fewer available ambulances. We also calculated the number of ambulances required for a robust ambulance operation strategy where the number of zero zones does not change over the planning horizon. This confirmed that ambulance operations managers need to comprehensively consider demand coverage, the number of zero zones, and the economics of introducing ambulances. The study we conducted can be extended to various future studies. For example, we conducted our study in three boroughs as a problem size limitation. However, Seoul comprises 25 boroughs, and future research could encompass larger-scale problem-solving methodologies, such as the entire city of Seoul. Additionally, there is a high correlation between ambulance dispatch time and traffic volume, and we used traffic volume as an average value. Future research could adopt a stochastic approach to traffic volume for more-accurate modeling. Regarding emergency demand, we based our analysis on historical accident data. Future research could incorporate probabilistic modeling of ambulance demand, taking into account demographic information such as disease outbreak history, the number of people, and their ages by borough. With a designed model, it can be extended to optimize ambulance deployment to efficiently cover maximum demand. Conceptualization, S.K. and T.C. ; methodology, S.K. and T.C. ; software, S.K. ; validation, T.C. ; formal analysis, S.K. ; investigation, S.K. ; resources, S.K. ; data curation, S.K. ; writing--original draft preparation, S.K. ; writing--review and editing, T.C. ; visualization, S.K. ; supervision, T.C. ; project administration, S.K. ; funding acquisition, T.C. All authors have read and agreed to the published version of the manuscript. This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. NRF-2021R1F1A105930213) and also supported by the \"National R&D Project for Smart Construction Technology (No. 23 SMIP-A158708-04)\" funded by the Korea Agency for Infrastructure Technology Advancement under the Ministry of Land, Infrastructure and Transport and managed by the Korea Expressway Corporation. This research was also supported by the Korea Institute for Advancement of Technology (KIAT) grant funded by the Korean Government (MOTIE) (The Competency Development Program for Industry Specialist) under Grant P0008691. This research was also supported by the Seoul Data Fellowship funded by the Seoul Metropolitan Government in 2023. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(P_{\text{r}}\)} & \multirow{2}{*}{**Before**} & \multicolumn{6}{c}{**Mathematical Model**} \\ \cline{3-8}  & & **March–May** & **June–August** & **September–November** & **December–February** & **Average** \\ \hline
15 & 52 & 29 & 52 & 52 & 52 & 46.25 \\
16 & 52 & 29 & 52 & 52 & 52 & 46.25 \\
17 & 52 & 52 & 40 & 40 & 26 & 39.5 \\
18 & 52 & 29 & 50 & 50 & 50 & 44.75 \\
19 & 52 & 38 & 38 & 38 & 38 & 38 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Seasonal changes in the number of zero zones due to changes in the number of ambulances in Seongdong-gu. **Institutional Review Board Statement:** Not applicable.