## 4 A Real-Case Scenario Application of the Proposed Algorithm
\begin{table}
\begin{tabular}{c c c c c c} \hline
**TW1** & **Number of** & **Number of** & **Activations** & **Deactivations** & \\
**Requested Operators** & **Operations** & & & & \\ \hline
**8:00-10:00** & 9 & 22 & 11 & 11 & \\
**120 min** & & & & & **Allocated** & **Not Allocated** \\  & & & & & **Time (min)** & **Time (min)** \\ \hline  & & & & & & \\ \hline  & & & & & & \\ \hline  & & & & & & \\ \hline  & & & & & & \\ \hline  & & & & & & \\ \hline  & & & & & & \\ \hline  & & & & & & \\ \hline  & & & & & & \\ \end{tabular}
\end{table} 
Table 3: Solution(4) provided by the proposed algorithm for TW1. The comparison deals with the problem, which as previously described is composed of 54 activations and 51 deactivations (reported in Table 2). Table 7 reports the results of the comparison. In particularly, there is an interesting decrease in running time (the computation time in minutes) as the total running time of the previous algorithm is 8.5 min while the proposed algorithm is completed in 3 min. Clearly, the difference between the two running times depends on the fact that the first algorithm takes into account more constraints with respect to the second solution, such as:  
* The load capacity (difficulty level of interventions) for the vehicle: the vehicle has a strict capacity, there is a maximum daily score per vehicle;
* The workload for a worker: it takes into account the maximum daily score per operator, the maximum score per time window and additionally the maximum score per type of operation. In light of the explanation above, it is important to point out that the solution provided by the proposed algorithm is clearly unfavorable. As Table 7 shows, the previous algorithm requires 9 operators and a total workload of 2673.2 while the current algorithm proposes 13 operators with a total workload of 2809.5. Furthermore, the imbalance increases from 182.9 min per operator per day in the previous case to 263.8 min in the case of the proposed algorithm. The analyzed operations (51 activations and 54 deactivations) represent the real data set analyzed and managed by the pilot company. In terms of time performance, by using a heuristic approach, a 'linear' increase in computational time would be expected in the case of a greater number of operations to be managed. Here, it is important to note that the proposed approach stems from the evident limitations of a previous math-heuristic approach that the authors developed to address the same problem. After almost a year of the pilot phase, the company showed difficulties in setting up and maintaining the set of constraints, as well as in adding or removing constraints and in managing frequent variations and unforeseen events occurring during day-by-day operations. Hence, the proposed approach is less 'optimal' (by using a set of heuristics) but allows the company to iteratively re-allocate operators to modified conditions in less time and in an easier way, thus, providing a more robust and effective solution to the real-time scenario. The benefits of the proposed approach are not just about pure performance but are related to its usability and applicability (less computational \begin{table}
\begin{tabular}{c c} \hline \hline
**ID** & **Time Window** \\ \hline
62 & TW1 \\
18 & TW1 \\
12 & TW1 \\
67 & TW2 \\
6 & TW2 \\
61 & TW3 \\
10 & TW3 \\
25 & TW4 \\
29 & TW5 \\
32 & TW6 \\
78 & TW6 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Dispatching list assigned to operator 8. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Number of** & **Total Daily** & **Daily Imbalance per** & **Running Time** \\  & **Operators** & **Workload (min)** & **Operator (min)** & **(min)** \\ \hline [PERSON] et al. 2018 & 9 & 2673.2 & 182.9 & 12.7 \\ Proposed algorithm & 13 & 2809.5 & 263.8 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison between the previous and the current work. time, less constraints to be managed by adopting an appropriate simplification, better reactivity) and the ability to dynamically generate solution routes.