\chapter*{Introduction}
\addcontentsline{toc}{chapter}{Introduction}
\chaptermark{Introduction}

%\section*{Section of Introduction}
%\addcontentsline{toc}{section}{Section of Introduction}

In every city, urban dwellers have to travel inside a city, for example they have to work, spend time with friends, buy groceries, etc.
The inhabitant's travels are made either on foot, with a (motor)bike, with a private car or with public transportation services (buses, subway, trains).
However with the increased congestion of city streets and the need to reduce pollution and CO$_2$ emissions from transports such as private cars, new services emerged, mostly in North American and Europe, with the objective of satisfying the need for trips inside the city while keeping negative effects of private vehicles' utilization to the minimum.
Carsharing services are one of several services that emerged: they offer cars to inhabitants that can be rented for a private usage at any time for a fee lower than a taxi service.
Carsharing services allow any driver to rent a car for a urban usage at any time, without the need to book in advance or to get the keys of the vehicle in a standard car rental agency.
The cars are dedicated to a city, meaning that a user can only rent it and drop it off in a given city.
With the objective to replace the inconvenience of car usage inside the cities, such services can reduce the car ownership of city dwellers~\cite{martin_impact_2010,giesel_impact_2016} and can also reduce C0$_2$ emissions when electric vehicles are offered by the service~\cite{firnkorn_what_2011,chen_carsharings_2016}.

However this new type of service has not yet reached its maturity, \emph{Autolib} in Paris (Figure~\ref{fig:ch0_autolib}) is an example of a carsharing service deployed and being shut down after several years due to profitability issues.
The fleet of vehicles accessible by the customers of such services needs to be monitored every day, either to make maintenance on the vehicles or to recharge the battery of electric vehicles.
Cars that are put back into service inside the city have to be placed carefully since the demand for this type of transportation is not uniform within the city.
The need to be able to place the whole fleet correctly arises, the more the cars are used by the customers the more profitable the service is.
Since the demand for this kind of service is not uniform in the city, hot spots and cold spots of demand shift the spatial distribution of the fleet towards an \textquote{un-optimal} distribution, i.e cars can be taken out of a busy city center towards peripheral areas of the city where the cars are less used and tend to accumulate unused.
For this reason, the objective of this thesis is to help the operator of carsharing services \emph{Free2Move} to better relocate its cars to make the service profitable enough.

\begin{figure}[!b]
    \centering
        \includegraphics[width=0.8\textwidth]{figure/ch0_autolib.jpeg}
        \caption[Autolib Paris Vehicles]{The one-way station-based carsharing service named \emph{Autolib} was available between 2011 and 2018. Each car on the map represent a station where cars can be returned, the car color designates the number of available reserved parking lots.\textsuperscript{1}}
        \small\textsuperscript{1}\emph{Carte interactive des stations Autolib' en Île-de-France} from \emph{www.data.gouv.fr}
        \label{fig:ch0_autolib}
\end{figure}

\paragraph{Types of Carsharing Services.}
There exist three different kinds of carsharing services.
Each type has been developed to alleviate constraints from previous carsharing types.
They still have common characteristics like the possibility to offer multiple types of cars (city cars, sedans, etc.) or the rent price, based either on the number of minutes of car usage, on the distance traveled by the customer or a combination of both.
Furthermore, carsharing services can take advantages of electrical vehicles in urban areas, offer only thermal vehicles or a combination of both.

The first type of carsharing service is called \emph{round-trip}, it allows customers to pick a car from any dedicated station of the service and return the vehicle \emph{in the same station}.
A dedicated station is a group of parking lots in the street reserved for the service customers and accessible for them.
The main example of this kind of carsharing is a brand named \emph{ZipCar} which is operating mainly in the U.S. and in Canada in over a hundred cities with more than ten thousand vehicles distributed among those cities.
A typical use case is a user renting a car near his/her home to do some shopping in the city center before going back hours later to his/her home.
However this kind of carsharing makes it impossible for a customer to take a car near his/her home and drive to his/her workplace by returning the car near it.
The customer should either rent the car until coming back to his/her home or simply take another means of transportation for the trip.

This constraint was alleviated by the second type of carsharing system called \emph{one-way} carsharing.
In this kind of service, the user is allowed to rent a vehicle from a station as in the \emph{round trip} type of service. 
But instead of being forced to return it in the same station, the customer is able to drop it in any other station, including the station where the vehicle was picked first.
A French example of this type of carsharing was \emph{Autolib}, it ran its service inside the urban area of Paris until late-2019.
In the case of one-way carsharing, even if it is possible for a customer to commute with a car of the service from home to the workplace, the location of each station still limits his/her mobility. 
The stations have to be placed by the operator \textquote{optimally}.
Indeed, the need to take and return the car inside designated stations weaken the user ability to move freely in the town: the customer cannot directly drop the car in front of the place he wants to stop.

\begin{figure}[!b]
    \centering
        \includegraphics[width=0.8\textwidth]{figure/ch0_free2move.jpg}
        \caption[Free2Move Paris Vehicles]{Example of free-floating carsharing service with Free2Move in Paris with its cars parked on previously reserved parking lots of the late \emph{Autolib} station-based carsharing service in Paris.\textsuperscript{1}}
        \small\textsuperscript{1}Tiraden, CC BY-SA 4.0, via Wikimedia Commons
        \label{fig:ch0_free2move}
\end{figure}

Finally, \emph{free-floating} carsharing service is the last type of carsharing which removes the need to have stations designated by the operator.
In this kind of service, the cars are parked on normal parking lots which are not reserved to the carsharing service.
Usually the operator of the service has an agreement with the city council: the operator pays a fixed amount annually to be able to park cars inside the city so customers do not have to worry about paying parking lots fees.
If electrical vehicles are used, the service might still offer stations to its customers to recharge the vehicles, but it does not force the user to leave a car at those stations.
Furthermore, the service might offer discounts to customers who return a car with a low battery charge to a charge station.
Some services such as \emph{Communauto} in Montréal thus offers a hybrid service, with cars both in \emph{free-floating} mode and in \emph{round-trip} mode with dedicated stations.
Furthermore, the main example of free-floating carsharing operators are \emph{Car2Go} and \emph{Free2Move} with cars in numerous cities around the world, mainly in Europe and North America.
Even if this type of carsharing system is very customer-friendly because of the lack of stations, it does not alleviate the need for cars to be relocated within the city to counter a possible demand imbalance.
The relocation decisions in this kind of carsharing can be harder and more complex since the user might take or return cars anywhere in the city and not only in dedicated stations of the service.

\paragraph{Carsharing Context.} 
This thesis has been motivated by the need of the company \emph{Stellantis}, the sponsor of this thesis, to improve the carsharing services of its brand \emph{Free2Move}. 
\emph{Free2Move} offers a free-floating carsharing service in several cities such as Paris, Washington, Madrid or other cities. 
While other services might open in the future, the optimization of the parameters for a new service is outside the scope of of this thesis.
The objective of this thesis concerns the improvement of an already existing free-floating carsharing service.
This kind of service can be improved in numerous ways, such as increasing the number of trips, the customer satisfaction or even optimizing the number of vehicles.
In the case of \emph{Free2Move}, the aim is to increase the average car utilization.
Since car utilization is time-based, there exist two ways to increase this average car utilization.
First it is possible to make the customer rent cars for a longer period of time and second it is possible to increase the number of bookings so cars are in general used more often.
While the operator can propose price cuts for a high utilization of the service in order to improve the length of trips, if most of the vehicles are being located in areas of the cities with a low demand overall, then their utilization might be hindered.
Thus the optimization of the vehicle fleet position is the main objective that should be accomplished to increase the utilization of the service, for example by making sure that customers do not have to walk too far to get a car.

\paragraph{Contribution.}
The main contribution of this thesis lies in the proposition of a methodology in order to increase the car fleet utilization at the global level.
This methodology has been created with the aim to be used by \emph{Free2Move}. 
Since real constraints linked to the physical service operator had to be taken into account for the development of this methodology, it is only possible to relocate cars \emph{during the night} and the number of cars that can be relocated is limited by the number of dedicated staff, also called \emph{jockeys}.
The main contribution is to compute the ideal car placement to be reached for the next morning, while taking into account constraints about the relocation costs and the jockey relocation capacity, in order to optimize the fleet utilization of the free-floating carsharing service~\cite{martin_prediction_2021,martin_optimisation_2022}.
The reason for the morning placement of the fleet is to counterbalance the demand imbalance which has changed the distribution of cars in the city since the last time the fleet has been relocated by the staff operator.
A two-step methodology is proposed in order to produce the result stated earlier.
The first step consists in predicting the future car utilization the next day according to the car position in the city.
Then the second step takes into account the utilization prediction of all the possible car positions as well as the distribution of the fleet before the relocation phase to then propose the ideal car fleet distribution for the next morning.
The contribution of this thesis has been published as two conference articles in: 
\begin{enumerate}
    \item Gregory Martin et al., \textquote{Prediction-Based Fleet Relocation for Free Floating Car Sharing Services}, \emph{2021 IEEE 33rd International Conference on Tools with Artificial Intelligence (ICTAI)}, IEEE, 2021, pp. 1187-1191.
    \item Gregory Martin et al., \textquote{Optimisation du Positionnement de Voitures en Autopartage basée sur la Prédiction de leur Utilité}, \emph{Conférence Nationale en Intelligence Artificielle 2022 (CNIA 2022)}, 2022
\end{enumerate}

\paragraph{Thesis Outline.}
This thesis had been organized in five chapters.
In Chapter~\ref{ch:background} is depicted how carsharing services are being modeled within the literature and how this kind of service is used by the customers in order to model their behavior accurately.
Then a focus is made on the possible improvements made for carsharing services and in particular free-floating ones and how numerical optimization can support these ameliorations. 
After that, the state-of-the-art carsharing simulations and on other transportation simulations that can include carsharing, with the aim to evaluate with more precision the results of the methodology developed during the thesis. 
Finally, a last focus is made on state-of-the-art regression models that are used in the two-step proposed methodology.

Chapter~\ref{ch:data_analysis} presents the details about trips data provided by \emph{Free2Move} and exogenous data of the three services located in \emph{Madrid}, \emph{Paris} and \emph{Washington}.
Since those three datasets are used during the experimental evaluation, multiple analyses are made about daily utilization of the service and their spatial distribution.
Furthermore, a finer analysis on the customers of each service is made in order to determinate if the prediction of the fleet utilization can be based on such information.

Chapter~\ref{ch:method} presents the main contribution of this thesis, i.e. the two-step method predicting the car utilization before providing the ideal distribution of these cars for the next morning.
First, the modeling of the car usage is explained as well as how it is possible to predict the next day car utilization according to the car position in the city as well as other exogenous data.
Second, an explanation is made on how the placement of cars the night before the relocation phase and all predicted car utilization can be used in an integer linear programming model to find the next morning car placement.
Finally, a first evaluation of this method is made, in particular to find out which prediction model should be used to predict the next day's car utilization as well as to find out the methodology effectiveness when it is compared to the historical service utilization.

In Chapter~\ref{ch:simulation}, a second evaluation of the proposed methodology given in Chapter~\ref{ch:method} is performed. 
The objective is to evaluate the behavior and the performance of this methodology when it is used for several days in a row, which is not possible with the previous experimental setting.
Thus the simulator created for this experiment will be presented as well as how it actually simulates a carsharing service.
Several baselines will be exposed and their performance tested against the previously presented methodology in order to make the evaluation.

Finally, Chapter~\ref{ch:ab_testing} details a short A/B testing study made on the real carsharing service of \emph{Free2Move} in Madrid.
Indeed a simplified version of the methodology proposed in Chapter~\ref{ch:method} has been tested on the field with the help of the operational team managing the service in Madrid.
The conducted A/B testing proposed to compare a period A where the operational staff had made decisions about the relocations with a period B where the simplified version of the methodology is used to relocate the cars.
