# The Vehicle Routing Problem: State-of-the-Art Classification and Review
## 3 VRP and Its Variants
### VRP Variants
\begin{table}
\begin{tabular}{c c} \hline
**1. Type of Study** & **3.4. Number of Points of Origin** \\ \hline
2.1.1 known (deterministic) & 3.7. number of vehicles \\ \hline
2.1.2 partially known, partially probabilistic & 3.7.1 exactly \(n\) vehicles \\ \hline
2.2. load splitting constraint & 3.7.2 up to \(n\) vehicles \\ \hline
2.2.1 splitting allowed & 3.7.3 restriction on drivers/vehicle \\ \hline
2.2.2 splitting not allowed & 3.8. capacity consideration \\ \hline
2.3. customer service demand quantity & 3.8.1 limited capacity \\ \hline
2.3.1 deterministic & 3.8.2 unlimited capacity \\ \hline
2.3.2 stochastic & 3.9. vehicle homogeneity (capacity) \\ \hline
2.3.3 unknown & 3.9.1 similar vehicles \\ \hline
2.4. request times of new customers & 3.9.2 load-specific vehicles \\ \hline
2.4.1 deterministic & 3.9.3 heterogeneous vehicles \\ \hline
2.4.2 stochastic & 3.9.4 customer-specific vehicles \\ \hline
2.4.3 unknown & 3.10. travel time \\ \hline
2.5. on-site service/waiting times & 3.10.1 deterministic \\ \hline
2.5.1 deterministic & 3.10.2 function dependent \\ \hline
2.5.2 time dependent & 3.10.3 stochastic \\ \hline
2.5.3 vehicle type dependent & 3.10.4 unknown \\ \hline
2.5.4 stochastic & 3.11. transportation cost \\ \hline
2.5.5 unknown & 3.11.1 travel time dependent \\ \hline
2.6. time window structure & 3.11.2 distance dependent \\ \hline
2.6.1 soft time windows & 3.11.3 vehicle dependent \\ \hline
2.6.2 strict time windows & 3.11.4 operation dependent \\ \hline
2.6.3 mixture of both & 3.11.5 function of lateness \\ \hline
2.7. time horizon & 3.11.6 implied hazard/risk related \\ \hline
2.7.1 single period & 4. information characteristics \\ \hline
2.7.2 multiple periods & 4.1. evolution of information \\ \hline
2.8. backhauls & 4.1.1 static \\ \hline
2.8.1. nodes request simultaneous pickups and deliveries & 4.1.2 partially dynamic \\ \hline
2.8.2. nodes request either linehaul or backhaul service, but not both & 4.2 quality of information \\ \hline
2.9. node/arc covering constraints & 4.2.1 known (deterministic) \\ \hline
2.9.1 precedence and coupling constraints & 4.2.2 stochastic \\ \hline
2.9.2 subset covering constraints & 4.2.3 forecasted \\ \hline
2.9.3 recourse allowed & 4.2.4 unknown (real-time) \\ \hline
3. problem physical characteristics & 4.3. availability of information \\ \hline
3.1. transportation network design & 4.3.1 local \\ \hline
3.1.1 directed network & 4.3.2 global \\ \hline
3.1.2 undirected network & 4.4. processing of information \\ \hline
3.2 locations of addresses (customers) & 4.4.1 centralized \\ \hline
3.2.1 customers on nodes & 4.4.2 decentralized \\ \hline
3.2.2 arc routing instances & 5. data characteristics \\ \hline
3.3 geographical locations of customers & 5.1 data used \\ \hline
3.3.1 urban (scattered with a pattern) & 5.1.1 real-world data \\ \hline
3.3.2 rural (randomly scattered) & 5.1.2 synthetic data \\ \hline
3.3.3 mixed & 5.1.3 both real and synthetic data \\ \hline
5.2 no data used & 5.2 no data used \\ \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No. **} & \multirow{2}{*}{**Authors**} & \multicolumn{3}{c}{**Model Features**} \\ \cline{3-5}  & & **Customer-Related Aspects** & **Vehicle-Related Aspects** & **Depot-Related Aspects** \\ \hline
1 & \begin{tabular}{c} ([PERSON], [PERSON], \\ [PERSON], \& [PERSON] [14]) \\ \end{tabular}  & time windows & heterogeneous vehicles & single depot \\ \hline
2 & \begin{tabular}{c} ([PERSON], [PERSON], \& [PERSON] [15]) \\ \end{tabular}  & classical & truck and drone & single depot \\ \hline
3 & \begin{tabular}{c} ([PERSON], [PERSON], \& [PERSON] [16]) \\ \end{tabular}  & classical & electric vehicles & single depot \\ \hline
4 & \ \begin{tabular}{c} ([PERSON], [PERSON], \& [PERSON] [17]) \\ \end{tabular}  & time windows & homogeneous vehicles & \begin{tabular}{c} loading at the depot \\ simultaneously \\ \end{tabular}  \\ \hline
5 & \begin{tabular}{c} ([PERSON], [PERSON], \& [PERSON] [18]) \\ \end{tabular}