# Application of the Clark-Wright Method to Improve the Sustainability of the Logistic Chain
## 5 Results
### Savings Calculations  
New routes for waste collection to the sorting center were created using the developed software, with a total of 45 new routes, which is 20 routes less than the current route. The new routes were divided into three groups. The first group are the routes only routed within the central town of the district. This group of routes would serve 245 nodes out of a total of 303 nodes. The remaining unserved peaks would be served by a second group \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Vehicle**} & \multirow{2}{*}{**Monday**} & \multirow{2}{*}{**Tuesday**} & \multirow{2}{*}{**Wednesday**} & \multirow{2}{*}{**Thursday**} & \multirow{2}{*}{**Friday**} & \multirow{2}{*}{**Number of**} & \multirow{2}{*}{
\begin{tabular}{c} **Weekly** \\ **Performance** \\ **(km)** \\ \end{tabular} } \\  & & & & & & **Server Points** & **(km)** \\ \hline
1 & ZA1 & ZA10 & K8 & O3 & O12 & 69 & 226.9 \\
2 & ZA2 & ZA11 & K9 & O4 & O13 & 79 & 247.9 \\
3 & O14 & ZA3 & K1 & K10 & O5 & 73 & 290.8 \\
4 & O15 & ZA4 & K2 & K11 & O6 & 63 & 297.9 \\
5 & O7 & O16 & ZA5 & K3 & K12 & 79 & 249.9 \\
6 & O8 & O17 & ZA6 & K4 & K13 & 74 & 274.9 \\
7 & K14 & O1 & O18 & ZA7 & K5 & 59 & 280.9 \\
8 & O9 & O10 & O19 & ZA8 & K6 & 66 & 303.5 \\
9 & K7 & O2 & O11 & O20 & ZA9 & 77 & 279.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Proposal for the weekly circulation of vehicles. \begin{table}
\begin{tabular}{l r r r} \hline \hline \multicolumn{1}{c}{**Rout**} & \multicolumn{1}{c}{**Length (km)**} & \multicolumn{1}{c}{**Required Capacity**} & \multicolumn{1}{c}{**Number of Served Points**} \\ \hline K1 & & 71.5 & 120 & 13 \\ K2 & & 62.3 & 120 & 9 \\ K3 & & 36.4 & 120 & 14 \\ K4 & & 31.7 & 120 & 14 \\ K5 & & 38.7 & 120 & 8 \\ K6 & & 59.0 & 120 & 9 \\ K7 & & 16.8 & 119 & 12 \\ K8 & & 18.0 & 119 & 9 \\ K9 & & 26.0 & 118 & 7 \\ K10 & & 23.0 & 118 & 10 \\ K11 & & 56.0 & 118 & 9 \\ K12 & & 30.0 & 118 & 8 \\ K1 of routes, serving the area in the central town's surroundings and the district's central town. These routes would serve 58 nodes in the district's center and 82 in the surrounding area. The last group of routes is the routes in the surroundings of the central section of the selected district. These routes cover a total of 264 nodes. The new mileage when accepting the created journeys would be 2447 km. The proposal for the optimal collection routes for municipal waste has an impact on these indicators:  
Total Distance Saved--The original distance has already been mentioned above. Its total length is currently 4896 km/week. The new distance that would be traveled using the newly created routes is 2447 km/week, almost half the original distance. The total distance saved can be calculated using the following formula:  
\[\Delta L=L_{0}-L_{1} \tag{8}\]  
where:  
\(\Delta L\)--distance saved [km];  
\(L_{0}\)--original mileage [km];  
\(L_{1}\)--new distance traveled after applying the Clark-Wright method [km]. \[\Delta L=4896-2447\]  
\[\Delta L=2449\ \text{km}\]  
Savings on Fuel--To quantify the economic benefit of distance saved, it was first necessary to calculate the corresponding fuel consumption. The company provided data about the average consumption per vehicle, which is 60 liters/100 km. Fuel consumption can be calculated using the following formula:  
\[S=\frac{\Delta L}{100}\ *\ S_{F}\ *\ s \tag{9}\]  
where:  
\(S\)--savings on fuel [liters];  
\(S_{F}\)--fuel consumption rate [liters/100 km];  
\(S\)--rate per 1 liter of gasoline (price detected on 30 August 2024). The given equation is the basic calculation of fuel consumption related to the distance traveled (\(\Delta L\)). However, we also acknowledge that this calculation needs to be supplemented with a correction factor that would account for fuel consumption caused by frequent stops. This correction factor could include, for example, fuel consumption during idling while stopping for loading and unloading, and during vehicle acceleration.