## 4 Experimental Results and Discussion
### Discussion on Real-Life Implementation of the Algorithm  
Every algorithm presents specific advantages and disadvantages. However, regardless of the algorithm, when multiple VRP variants are involved in the optimization process, the computation time is increased. Heuristic algorithms used to be applied and implemented in routing and scheduling software, due to their ability to perform in a relatively limited search space and simultaneously produce efficient solutions in limited computing time [51]. On the other hand, metaheuristic algorithms operate a wider search space, but this does not necessarily mean that the computational time will significantly increase. The advances of technology and computer science give researchers the ability to produce near-optimal solutions, and in most cases better than those produced by heuristics. Therefore, metaheuristics should be considered for implementation in routing software solutions due to offering reliable and on-time deliveries to transportation companies.  
[PERSON] et al. [52], [PERSON] et al. [53] and [PERSON] et al. [54] described the design and requirements of various routing and scheduling software that need fast and efficient solutions both for the initial planning and for the rescheduling of deliveries. It is clear that practitioners and companies are looking for efficient algorithms to integrate into their software solutions for logistics operations. According to Tables 1-3, the proposed MOLNS algorithm offers near-optimal solutions in a reasonable time, while also having the ability to solve cases with a higher number of customers and rendering the algorithm ideal for the routing of vehicles and scheduling of deliveries in real-life cases. Therefore, the proposed algorithm can be implemented in a software solution, to solve the problem of routing and scheduling of deliveries effectively. That was the scope of the developed algorithm from the beginning and the current research proves that it is in line with this scope.  
As noted in the Introduction, information available to the planner commonly changes in real-life cases after the completion of the initial routing and scheduling. Consequently, a rapid rescheduling procedure that is fed with dynamic data becomes a necessity to create a viable real-life routing and rescheduling system. This becomes even more clear when considering that, in real-life cases, changes  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Problem** & **MOLNSNV** & **MOLNTD** & **BPNV** & **BPTD** & \begin{tabular}{c} **Time** \\ **(sec)** \\ \end{tabular} & \
\begin{tabular}{c} **Deviation in** \\ **the NV (\%)** \\ \end{tabular} &
\begin{tabular}{c} **Deviation in** \\ **the TD (\%)** \\ \end{tabular} \\ \hline C1 & 100.2 & 460,310.32 & 94.2 & 416,797.49 & 624 & 6.37\% & 10.44\% \\ C2 & 31.8 & 181,653.35 & 28.9 & 166,304.04 & 559 & 10.03\% & 9.23\% \\ R1 & 95.8 & 525,362.56 & 91.9 & 470,041.69 & 800 & 4.24\% & 11.77\% \\ R2 & 20.2 & 314,856.25 & 19 & 288,457.54 & 810 & 6.32\% & 9.15\% \\ RC1 & 93.6 & 486,596.35 & 90 & 439,493.53 & 558 & 4.00\% & 10.72\% \\ RC2 & 19.8 & 268,569.78 & 18.2 & 239,221.86 & 741 & 8.79\% & 12.27\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Gehring and Homberger’s instances with 1000 customers: comparison of our MOLNS with the best-published results.  
may even occur while vehicles are on the road to deliver the orders, and, therefore, rapid rescheduling becomes mandatory. The algorithm presented in this paper can also support the dynamic aspect of the VRPTW, as the removal and insertion operators of the MOLNS algorithm can handle changes of the input data, such as travel times between nodes. Hence, the algorithm can be applied for both the initial plan and the rescheduling procedure by applying some minor modifications.