# DMRVR: Dynamic Milk-Run Vehicle Routing Solution Using Fog-Based Vehicular Ad Hoc Networks
## 4 Evaluation of the DMRVR Solution
### Evaluating Efficiency in the Dynamic Vehicle Routing  
The average time to perform the component collecting route was computed, plus the tardiness time observed at the supplier's factory. The average time to perform the route is computed via Equation (8). The collecting route is considered efficient when \(T_{R}\), given by (8), does not exceed the JIT upper restriction:  
\[T_{R}=t_{OEM}^{(1)}+t_{1}^{(tv)}+\sum_{i=1}^{q}\left[t_{i}^{(tv)}+t_{i}^{(trd )}+t_{i}^{(ld)}\right]+t_{q+1}^{(tx)}+t_{OEM}^{(2)} \tag{8}\]  
where \(t_{OEM}^{(1)}\) is the loading time of the empty container into the vehicle, \(t_{1}^{(tx)}\) is the vehicle displacement time from the logistics operator to the first supplier, \(t_{i}^{(tx)}\) is the time to move the vehicle from supplier \(i\) to supplier \(i+1\), \(t_{i}^{(trd)}\) is the production tardiness at supplier \(i\), if any, \(t_{i}^{(ld)}\) is the vehicle loading time at the supplier \(i\), \(t_{q+1}^{(tx)}\) is the return time to the OEM company, and \(t_{OEM}^{(2)}\) is the unloading time at the OEM main industry production line. We have used a density upper value of 3900 vehicles to analyze the vehicle routing efficiency. This density value was assumed because such a value was close to the logistic situation observed in LuST. A total of 30 cases were ran in the simulation. The results on the dynamic vehicle routing efficiency have been compared with the results shown in [10], employing the same simulators and variables. Table 8 depicts such results. The expected time to perform the pickup route in the DMRVR model was 164 min, while, in [10], it was 176 min. However, the 180 min upper limit was surpassed in 37% of the ran cases in [10]. Such results indicated a non-compliance situation regarding the agreement between the OEM leader firm and the logistics operator, also reflecting a disruption in the main OEM production line. On the other hand, the utilization of an auxiliary pickup vehicle led to a higher total cost along the milk-run operation. In addition, the DMRVR used an auxiliary pickup vehicle in 86% of our simulation runs, as compared with 87% in [10]. Comparing further, the expected time delay that the collecting vehicle had to wait at the suppliers' docks was 8 min in our model, against 14 min in [10]. In addition, DMRVR was able to offer anticipated information to the logistics operator about supplier expected tardiness in their manufacturing plant. Such information is sent further to the collecting vehicle, possibly before the latter arrives at the supplier dock. Thus, the logistics operator will be to make possible operational adjustments in order to reduce delays in the overall milk-run time. This feature represents an advantage point as compared to [10]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Density Peaks** & **Simulation Time (Hours)** \\ \hline
600 & 2 \\
1200 & 10 \\
3900 & 130 \\
4600 & 195 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average simulation time. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Work** & **Average** & **Average** & **Use of the** \\
**Route Time** & **Delay** & **Auxiliary Pickup** \\ \hline DMRVR & 160 & 8 & 86\% \\
[10] & 176 & 14 & 87\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Dynamic vehicle routing efficiency. In 20% of the simulated cases, DMRVR has taken out one supplier from the milk-run setting as a result of the accumulated suppliers delays and traffic congestion. Such information was not sent to the logistics operator, leading to a fault since an auxiliary vehicle was not sent by the latter to collect the components from the supplier, with a possible negative impact on the OEM overall performance. Solving this kind of problem, which can negatively affect the OEM supply chain, we developed a queuing improvement in the DMRVR framework. Whenever a _NotifyWithdrawal_ message is broadcasted in the _LogisticsService_, the message is inserted in the queue.