# Optimized Travel Itineraries: Combining Mandatory Visits and Personalized Activities
## 4 Computational Study
### Real Case Instances from Tak, Thailand
#### 4.2.2 Example of the Travel Itinerary Obtained by the Proposed Algorithm  
From the Tak case study, we provide an example of the results from the dataset Tak1. In this dataset, there are 108 locations. The mandatory locations that must be visited every day (\(N_{d}\)) consists of 44 locations, \(N_{d}=\{65,\ 66,\ \ldots,\ 108\}\). There are also three mandatory locations that can be visited at any time during the trip, \(N_{m}=\{28,\ 46,\ 49\}\). Additionally, the mandatory activity in \(A_{m}\) is the nature-based activities, \(A_{m}=\{1\}\). In this case, at least one location in \(N_{m}\) and \(N_{d}\) should be visited (\(l=1\) and \(n=1\)). The results from the model suggest a travel itinerary for tourists on a one-day trip, as illustrated in Table 6 and the route in Figure 10. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Sequence of** \\ **Locations** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Locations** \\ **No.** \\ \end{tabular} } & \multicolumn{2}{c}{**Location Detail**} & \multirow{2}{*}{\
\begin{tabular}{c} **Estimate** \\ **Arival Time** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Estimate** \\ **Visiting Time** \\ \end{tabular} } \\ \cline{5-8}  & & & & & & 24 h & 6.00 a.m. & - \\
2 & 32 & Astonishing hill &
\begin{tabular}{c} Nature-based \\ activities \\ \end{tabular} & 1.83 & 24 h & 8.00 a.m. & 1 h \\
3 & 86 & Ban Tong Kitchen & Restaurant & 2.97 & 10.00 a.m.–9.00 p.m. & 11.30 a.m. & 1 h \\
4 & 28 & Bhumibol Dam &
\begin{tabular}{c} Nature-based \\ activities \\ \end{tabular} & 2.98 & 6.00 a.m.–6.00 p.m. & 13.00 a.m. & 2 h \\
5 & 66 &
\begin{tabular}{c} Mac Bang Hua Deet \\ No Nodes \\ \end{tabular} & Restaurant & 2.91 & 6.00 a.m.–8.00 p.m. & 17.00 p.m. & 1 h \\
6 & 0 & Shrine of [PERSON] & & & 24 h & 18.00 p.m. & - \\ \hline \multicolumn{8}{c}{Total Score} & \multicolumn{2}{c}{10.69} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The travel itinerary for tourists on a one-day trip from the dataset Tak1. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Name** \\ \end{tabular}  } & \multicolumn{6}{c}{**Objective Value**} \\ \cline{2-10}  & \multicolumn{2}{c}{\(p=1\)} & \multicolumn{2}{c}{**Gap (\%)**} & \multicolumn{2}{c}{\(p=2\)} & \multirow{2}{*}{ \begin{tabular}{c} **Gap (\%)** \\ **ANSA-1** \\ \end{tabular}  } & \multicolumn{2}{c}{**(\(p=3\)**)**} & \multirow{2}{*}{ \begin{tabular}{c} **Gap (\%)** \\ **ANSA-2** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Gap (\%)** \\ **ANSA-1** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Gap (\%)** \\ **ANSA-2** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **Gap (\%)** \\ **ANSA-1** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Gap (\%)** \\ **ANSA-2** \\ \end{tabular}  } \\ \hline Tak1 & 7.63 & 10.69 & 40.10 & 43.9 & 44.66 & 1.73 & 69.79 & 75.31 & 7.91 \\ Tak2 & 12.74 & 11.71 & \(-\)8.08 & 46.86 & 43.12 & \(-\)7.98 & 68.54 & 69.63 & 1  
The proposed itinerary begins and ends at the Shrine of King Taksin. Following this, tourists are suggested to visit the Astonishing Hill for nature-based activities. For lunch, they will dine at Ban Tong Kitchen. The itinerary continues with a visit to the Bhumibol Dam in the early afternoon, providing visitors with an extended opportunity to appreciate the scenic natural environment. As evening approaches, tourists will enjoy a meal at Mae Bang Hua Deet Noodles before making a final visit to the Shrine of [PERSON]. Overall, the itinerary is structured to maximize enjoyment and efficiency. In this trip, all constraints of the proposed algorithm are satisfied. Ban Tong Kitchen (Location 86) and Mae Bang Hua Deet Noodles (Location 66) are part of the set of mandatory locations that must be visited every day. The Bhumibol Dam (Location 28) is included as a requested mandatory location that can be visited at any time during the trip.