\appendix

\chapter{Appendix - Relocation Strategies Performances}

\section{Comparison of Operator-based Relocations}

\subsection{Madrid Case}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_madrid_utility_bfp.jpeg}}
        \caption[Madrid Simulation Utility Performance Expe1 BFP Placement]{Curves of the expected \emph{Utility} (in minutes) of the \emph{Madrid} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_madrid_utility_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_madrid_utility_wfp.jpeg}}
        \caption[Madrid Simulation Utility Performance Expe1 WFP Placement]{Curves of the expected \emph{Utility} (in minutes) of the \emph{Madrid} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_madrid_utility_wfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_madrid_profit_bfp.jpeg}}
        \caption[Madrid Simulation Profit Performance Expe1 BFP Placement]{Curves of the expected \emph{Profit} (in euros) of the \emph{Madrid} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_madrid_profit_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_madrid_profit_wfp.jpeg}}
        \caption[Madrid Simulation Profit Performance Expe1 WFP Placement]{Curves of the expected \emph{Profit} (in euros) of the \emph{Madrid} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_madrid_profit_wfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_madrid_cost_bfp.jpeg}}
        \caption[Madrid Simulation Cost Performance Expe1 BFP Placement]{Curves of the expected \emph{Cost} (in euros) incurred by the tested relocation strategies \emph{OR-Greedy} and \emph{OR-Optim} and their variants. Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_madrid_cost_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_madrid_cost_wfp.jpeg}}
        \caption[Madrid Simulation Cost Performance Expe1 WFP Placement]{Curves of the expected \emph{Cost} (in euros) incurred by the tested relocation strategies \emph{OR-Greedy} and \emph{OR-Optim} and their variants. Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_madrid_cost_wfp}
\end{figure}

\FloatBarrier
\subsection{Paris Case}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_paris_utility_bfp.jpeg}}
        \caption[Paris Simulation Utility Performance Expe1 BFP Placement]{Curves of the expected \emph{Utility} (in minutes) of the \emph{Paris} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_paris_utility_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_paris_utility_wfp.jpeg}}
        \caption[Paris Simulation Utility Performance Expe1 WFP Placement]{Curves of the expected \emph{Utility} (in minutes) of the \emph{Paris} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_paris_utility_wfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_paris_profit_bfp.jpeg}}
        \caption[Paris Simulation Profit Performance Expe1 BFP Placement]{Curves of the expected \emph{Profit} (in euros) of the \emph{Paris} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_paris_profit_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_paris_profit_wfp.jpeg}}
        \caption[Paris Simulation Profit Performance Expe1 WFP Placement]{Curves of the expected \emph{Profit} (in euros) of the \emph{Paris} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_paris_profit_wfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_paris_cost_bfp.jpeg}}
        \caption[Paris Simulation Cost Performance Expe1 BFP Placement]{Curves of the expected \emph{Cost} (in euros) incurred by the tested relocation strategies \emph{OR-Greedy} and \emph{OR-Optim} and their variants. Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_paris_cost_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_paris_cost_wfp.jpeg}}
        \caption[Paris Simulation Cost Performance Expe1 WFP Placement]{Curves of the expected \emph{Cost} (in euros) incurred by the tested relocation strategies \emph{OR-Greedy} and \emph{OR-Optim} and their variants. Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_paris_cost_wfp}
\end{figure}


\FloatBarrier
\subsection{Washington Case}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_washington_utility_bfp.jpeg}}
        \caption[Washington Simulation Utility Performance Expe1 BFP Placement]{Curves of the expected \emph{Utility} (in minutes) of the \emph{Washington} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_washington_utility_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_washington_utility_wfp.jpeg}}
        \caption[Washington Simulation Utility Performance Expe1 WFP Placement]{Curves of the expected \emph{Utility} (in minutes) of the \emph{Washington} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_washington_utility_wfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_washington_profit_bfp.jpeg}}
        \caption[Washington Simulation Profit Performance Expe1 BFP Placement]{Curves of the expected \emph{Profit} (in euros) of the \emph{Washington} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_washington_profit_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_washington_profit_wfp.jpeg}}
        \caption[Washington Simulation Profit Performance Expe1 WFP Placement]{Curves of the expected \emph{Profit} (in euros) of the \emph{Washington} service when the operator does nothing (\emph{NoAction}), or use the \emph{OR-Greedy} or \emph{OR-Optim} relocation strategies (with their variant). Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_washington_profit_wfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_washington_cost_bfp.jpeg}}
        \caption[Washington Simulation Cost Performance Expe1 BFP Placement]{Curves of the expected \emph{Cost} (in euros) incurred by the tested relocation strategies \emph{OR-Greedy} and \emph{OR-Optim} and their variants. Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_washington_cost_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu1_washington_cost_wfp.jpeg}}
        \caption[Washington Simulation Cost Performance Expe1 WFP Placement]{Curves of the expected \emph{Cost} (in euros) incurred by the tested relocation strategies \emph{OR-Greedy} and \emph{OR-Optim} and their variants. Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu1_washington_cost_wfp}
\end{figure}

\FloatBarrier
\section{Comparison of Customer-based Relocations}

\subsection{Paris Case}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=1\textwidth]{figure/ch4_expesimu3_paris_urmax.jpeg}}
        \caption[URMax Last Fleet Distribution WFP Paris]{Heatmap of the fleet distribution in \emph{Paris} after 30 days of simulation. Green cells denotes a low number of cars in the cells and red is a high amount. The number is each cell is the number of cars in the cell.}
        \label{fig:ch4_expesimu3_paris_urmax}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu3_paris_utility_bfp.jpeg}}
        \caption[Paris Simulation Utility Performance Expe3 BFP Placement]{Curves of the expected \emph{Utility} (in minutes) of the \emph{Paris} service when the operator does nothing (\emph{NoAction}), use \emph{OR-Optim} relocation strategies or customer incentives (\emph{UR-Max}, \emph{UR-Heavy}, \emph{UR-Light}). Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu3_paris_utility_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu3_paris_utility_wfp.jpeg}}
        \caption[Paris Simulation Utility Performance Expe3 WFP Placement]{Curves of the expected \emph{Utility} (in minutes) of the \emph{Paris} service when the operator does nothing (\emph{NoAction}), use \emph{OR-Optim} relocation strategies or customer incentives (\emph{UR-Max}, \emph{UR-Heavy}, \emph{UR-Light}). Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu3_paris_utility_wfp}
\end{figure}

\FloatBarrier
\subsection{Washington Case}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.95\textwidth]{figure/ch4_expesimu3_washington_urmax.jpeg}}
        \caption[URMax Last Fleet Distribution WFP Washington]{Heatmap of the fleet distribution in \emph{Washington} after 30 days of simulation. Green cells denotes a low number of cars in the cells and red is a high amount. The number is each cell is the number of cars in the cell.}
        \label{fig:ch4_expesimu3_washington_urmax}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu3_washington_utility_bfp.jpeg}}
        \caption[Washington Simulation Utility Performance Expe3 BFP Placement]{Curves of the expected \emph{Utility} (in minutes) of the \emph{Washington} service when the operator does nothing (\emph{NoAction}), use \emph{OR-Optim} relocation strategies or customer incentives (\emph{UR-Max}, \emph{UR-Heavy}, \emph{UR-Light}). Fleet distribution initialization is following the \emph{Balanced First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu3_washington_utility_bfp}
\end{figure}

\begin{figure}[h]
    \centering
        \makebox[\textwidth][c]{\includegraphics[width=0.8\textwidth]{figure/ch4_expesimu3_washington_utility_wfp.jpeg}}
        \caption[Washington Simulation Utility Performance Expe3 WFP Placement]{Curves of the expected \emph{Utility} (in minutes) of the \emph{Washington} service when the operator does nothing (\emph{NoAction}), use \emph{OR-Optim} relocation strategies or customer incentives (\emph{UR-Max}, \emph{UR-Heavy}, \emph{UR-Light}). Fleet distribution initialization is following the \emph{Worst First Placement}. One x-tick is a Sunday.}
        \label{fig:ch4_expesimu3_washington_utility_wfp}
\end{figure}