## 3 Problem Description
### Road Type Characteristics  
The two different road types applied in this study, namely highways and slow roads, are represented by the notations \(\mathrm{Rd_{h}}\) and \(\mathrm{Rd_{g}}\), respectively, and the analyses of their characteristics are shown in Table 1.  
The problem in this study is solved based on the following assumptions:  
1. Only one truck delivers the goods.
2. The loading capacity of each truck is W (unit weight).
3. The turning angle is limited to less than 90 degrees when the truck is driving on \(\mathrm{Rd_{h}}\)  
\begin{table}
\begin{tabular}{l|l l} \hline \hline
**Characteristics** & \(\mathrm{Rd_{h}}\) & \(\mathrm{Rd_{g}}\) \\ \hline Speed & Faster & Slower \\ Turning angle & Limited & Not limited \\ Transportation lead time at equal distances & Shorter & Longer \\ Vehicle loading capacity & Lower & Higher \\ Number of distributions of equal quantity & More & Less \\ Tolls & Charge & Non-charge \\ \hline \hline \end{tabular}
\end{table}
Table 1: Transportation characteristics of two different road types.  
There is no limit to the turning angle when the truck is driving on \(\mathrm{Rd_{g}}\).  
The following information is further analyzed according to the transportation characteristics of the two different road types from Table 1:  
1. Transportation lead time at equal distances: The transportation lead time is longer for driving on \(\mathrm{Rd_{g}}\) because the speed is slower, while the transportation lead time is shorter for driving on \(\mathrm{Rd_{h}}\) because the speed is faster.
2. Turning angle: The turning angle is not limited for driving on \(\mathrm{Rd_{g}}\) because the speed is slower, and the turning angle of the truck can be large, while the turning angle is limited for driving on \(\mathrm{Rd_{h}}\) because the speed is faster, and there is a danger of overturning the truck if the angle of the truck is too large.
3. Vehicle loading capacity: The vehicle loading capacity is higher for driving on \(\mathrm{Rd_{g}}\) because there is no weight limit, while the vehicle loading capacity is lower for driving on \(\mathrm{Rd_{h}}\) because there is a weight limit.
4. Number of distributions of equal quantity: The number of distributions is less for driving on \(\mathrm{Rd_{g}}\) because the vehicle loading capacity is higher, and the amount of heavier cargo can be loaded on each departure truck, while the number of distributions is greater for driving on \(\mathrm{Rd_{h}}\) because the vehicle loading capacity is lower, and a small (light) quantity of cargo can be loaded on each truck. The following example offers a description:  
**Example**. Suppose that three (unit weight) goods need to be delivered, the load weight limits are three (unit weight) and two (unit weight) for vehicles driving on \(\mathrm{Rd_{h}}\) and \(\mathrm{Rd_{g}}\), respectively.  
**Solution**: The vehicle needs to run three times while driving on \(\mathrm{Rd_{h}}\) to transport all three (unit weight) goods to the destination because the first one can only carry two (unit weight) of the goods. Then, the second requires empty vehicles to return from the destination, and the third picks up the remaining good (unit weight) from the source node and transports it to the destination.  
The vehicle only needs to run one time while driving on \(\mathrm{Rd_{g}}\) to transport all three (unit weight) goods to the destination.