# Ambulance Locations in a Tiered Emergency Medical System in a City
## 3 Results
### Results for the LandScan Demand Model  
In this section we evaluate the performance of the location models based on the LandScan distribution of demand in the city of Presov. Table 1 presents the static criteria values for the following five models: \(p\)MP, MEXCLP with binary location variables, MEXCLP with integer location variables, ERTM, and MCLP. The last row of the table refers to the computing time. The models were solved using the commercial solver Xpress-MP run on a personal computer equipped with an Intel Core i7 processor with 1.60 GHz and 8 GB RAM. From the static viewpoint, no model outperforms the others unambiguously. The MCLP model results in the same locations of the stations as the \(p\)MP model, but proposes a different distribution of ALS and BLS ambulances. However, ambulance types do not affect the static criteria. In general, the models with response time objectives work better than the coverage objective models. Even the expected coverage within the 15 min threshold is better with the \(p\)MP, ERTM, and MCLP models than it is with the MEXCLP model. The MEXCLP model with integer variables allocated ambulances to three different station locations. Although its objective function value (the expected coverage within 8 min) is better than that of the MEXCLP model with binary variables, its overall performance is worse. Computer simulation is supposed to verify whether the dominance of the models with response time objectives holds in practice. The results of the simulation study for the city of Presov are in Table 2. The simulation experiment for one set of station locations consisted of 10 replications. One replication simulated 91 days of EMS performance. For response times, the mean values from 10 replications with 95% confidence intervals are reported. For coverage indicators, the mean values of 10 replications are given. The best values of the indicators are displayed in bold. In the first column, the simulation results for the current distribution of the stations are shown. As it is demonstrated, all models result in better EMS performance in comparison to the current distribution of the stations. The improvements in the average response times are statistically significant with regard to all patients, as well as to high-priority patients. The best average response time, regardless of the patient's priority, has been achieved by the ERTM model that reduces the current time by 62 s. The MCLP models exhibits the best improvement in the average response times for high-priority calls (a reduction by 79 s). Since critical patients are of the EMS's main concern, we consider the MCLP model as the \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Criterion** & \(p\)**MP** & \
\begin{tabular}{c} **MEXCLP** \\ **Binary** \\ \end{tabular} &
\begin{tabular}{c} **MEXCLP** \\ **Integer** \\ \end{tabular} & **ERTM** & **MCLP** \\ \hline Average response time (min) & 2.67 & 3.22 & 3.74 & 2.89 & 2.67 \\ Average expected response time (min) & 3.59 & 3.79 & 4.01 & 3.48 & 3.59 \\ Expected coverage within & 99.08 & 99.06 & 99.06 & 99.07 & 99.08 \\ Expected coverage within & 97.18 & 98.34 & 98.46 & 97.87 & 97.18 \\ Computing time (s) & 1.13 & 0.23 & 0.18 & 42.94 & 2.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Static evaluation of the location models, LandScan model of demand.