# Dynamic Multi-Compartment Vehicle Routing Problem for Smart Waste Collection +
## Experimental Study
### Real-World Study
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Hour** & **Station** & **Bin** & \
\begin{tabular}{c} **Container** \\ **Capacity (m\({}^{3}\))** \\ \end{tabular} & **Filling Level (\%)** &
\begin{tabular}{c} **Amount** \\ **Collected (kg)** \\ \end{tabular} \\ \hline \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\
19:25:20 & 1590 & P0800 & 2.5 & 0\% & 0 \\
19:25:33 & 1590 & P2257 & 2.5 & 2.5\% & 25 \\
19:27:00 & 578 & T\_P0021 & 2.5 & 0\% & 0 \\
19:29:48 & 2293 & P2306 & 2.5 & 50\% & 50 \\
19:39:38 & 574 & P0438 & 2.5 & 50\% & 50 \\ \hline \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Part of the visit sequence of a shift. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Waste** & \
\begin{tabular}{c} **Density Inside the Bins** \\ **(kg/m\({}^{3}\))** \\ \end{tabular} &
\begin{tabular}{c} **Density in the Collection** \\ **Vehicles (kg/m\({}^{3}\))** \\ \end{tabular} \\ \hline Paper and/Cardboard & 40 & 250 \\ Plastic and/Metal & 20 & 150 \\ Glass & 300 & 600 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Density of the materials collected by Valorsul inside the respective bins, and inside collection vehicles. real-time information on the filling levels of the bins). Route 6 with 68 containers, route 11 with 74 containers, and route 13 with 84 containers, totaling of 226 containers. The scalar data of the study are those presented in Table 7. \(C_{ij}\) is the cost of travel per distance unit, including fuel consumption, vehicle maintenance, and the salary of the collection team. \(q_{i}\) is the amount of waste at bin \(i\), (considering the density of paper/cardboard), simulates the values the sensors will read and transmit daily. To apply the resolution method, we use the bin's fill levels registered by the collection team after visiting these bins plus an expected accumulation rate per bin \(i\). This accumulation rate was calculated by dividing the bin fill levels recorded by the collection team by the number of days that passed after the previous day the bins were collected ([PERSON] et al. [10]). For Valorsul, the types of waste are not always in the same station; there are other routes to collect plastic/metal and glass. To apply our model and our proposed approach, we assume that each station contains two bins (one for paper/cardboard, one for Metal/Plastic), and we use a two- compartment vehicle. Table 6 shows the data from Valorsul, and we add some more data for it to be applied to our problem (from the data illustrated by [PERSON] [29]). [PERSON] et al. considered a planning period of 30 days to collect the paper/cardboard; the profit obtained by the Valorsul for the three routes is presented in Table 8. During the planning period, routes 6 and 11 were twice repeated, route 13 four times, and 620 bins were visited, with 12% empty and 1% overflowing. In these eight routes, the waste collected amounted to 17,000 kg, and 1200 km were traveled, resulting in an average of around 15 kg per km traveled), and the vehicle utilization rate varied between 46% and 67%. Since we do not have data in the literature on the collection of Plastic/Metal, we will propose data presented in Table 9. On these eight routes, it is assumed that the waste \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Values** & **Source** \\ \hline \(C_{ij}\) & \(1\,\epsilon/\text{km}\) & Valorsul \\ \hline \multirow{3}{*}{Q} & 4000 kg & Valorsul \\  & \(C_{dpC}\,=2500\) kg, & [PERSON] et al. [29] \\  & \(C_{dpM}\,=1500\) kg & [PERSON] et al. [29] \\ \hline \multirow{3}{*}{\(Cp_{w}\)} & \(Cp_{PC}\,=\)74 kg & [PERSON] et al. [10] \\  & \(Cp_{PM}\,=74\) kg & — \\ \hline \(q_{i}\) & Team records for day 1 & Valorsul \\ \hline \multirow{3}{*}{\(\rho_{w}\)} & \(\rho_{\text{PC}}\,=29.5\) kg/ m\({}^{3}\) & Valorsul \\  & \(p_{\text{PM}}\,=29.5\) kg/ m\({}^{3}\) & — \\ \hline \(d_{ij}\) & Adjusted Euclidian distance & [PERSON] et al. [10] \\ \hline S & 226 & Valorsul \\ \hline \hline \end{tabular}
\end{table}