# Day and Night: Locating the General Practitioner's Panel after Hours
## 3 Results
### Case Studies
#### 3.2.1. Halifax  
In the Halifax setting, there are 594 DAs and a total demand of 390,096 people. Figure 2 displays the geography of the included DAs.  
Tests were run for increments of 5, 20, 40, 60, and 200 regular facilities, with after-hours facilities increased in fifths. For example, the 60 regular facilities scenario was considered with 12, 24, 36, 48, and 60 after-hours facilities. In total, \(5\times 5=25\) facility placement scenarios were tested for each solution approach.  
Table 2 contains the results for each solution approach (independent, sequential, and simultaneous) and the time periods for one scenario in the Halifax setting. There are two rows for the sequential approach since this approach differs between regular to after hours (RtA) and after hours to regular (AtR). In the scenario used for this example, sixty facilities are located for the regular setting, and twelve are located for the after-hours setting.  
Figure 2: Halifax Dissemination Areas.  
By dividing the results in Table 2 by the total demand, the average distance travelled by each person is calculated, as shown in Table 3.  
The lower the results are, the better the solution. This is because a lower overall cost means that the demand (people in this case) need to travel less distance on average. It is expected that as \(p\) and \(p^{\prime}\) increase, the cost will go down. This is because locating more facilities allows facilities to be more spread out and closer to demand on average. This can be seen in Figure 3, which plots the cost in the independent setting against the number of facilities. This applies to both settings and each approach. If facilities are added, the cost is expected to decrease.  
In all cases, the least constrained approach, the independent approach, has the lowest costs, while the sequential approaches have higher costs than the simultaneous approach. A sample is shown in Table 4, where the independent approach is treated as the base case to calculate the difference in other cases.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Approach**} & \multicolumn{3}{c}{\(p\) = 60, \(p^{\prime}\) = 12} \\ \cline{2-4}  & **Day-Time** & **After-Hours** & **Total** \\ \hline Independent & 327,904 & 475,128 & 803,032 \\ Sequential (Rta) & 327,904 & 482,107 & 810,011 \\ Sequential (AtR) & 328,352 & 475,128 & 803,480 \\ Simultaneous & & & 803,277 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Halifax Total Cost (km).  
Figure 3: Halifax Regular Setting Independent Approach Cost by number of Facilities.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Approach**} & \multicolumn{3}{c}{\(p\) = 60, \(p^{\prime}\) = 12} \\ \cline{2-5}  & **Regular** & **After-Hours** & **Overall** & **Std. Deviation** \\ \hline Independent & 0.8365 & 1.2121 & 2.0486 & 15.9845 \\ Sequential (Rta) & 0.8365 & 1.2299 & 2.0664 & 16.0712 \\ Sequential (AtR) & 0.8376 & 1.2121 & 2.0497 & 15.9852 \\ Simultaneous & & & 2.0492 & 15.9855 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Halifax Average Cost Per Person (km).  
These results suggest that the approaches perform as expected relative to the degree to which they are each constrained.