tex: add content for part 1

latex/content.tex

@@ -3,9 +3,7 @@
 Bin packing is the process of packing a set of items of different sizes into
 containers of a fixed capacity in a way that minimizes the number of containers
 used. This has applications in many fields, such as logistics, where we want to
-optimize the storage and transport of items in boxes, containers, trucks, etc. In
+optimize the storage and transport of items in boxes, containers, trucks, etc.
-this paper, we will focus on one-dimensional bin packing, where we try to store
-items of different heights in a linear container.
 
 Building mathematical models for bin packing is useful in understanding the
 problem and in designing better algorithms, depending on the use case. An
@@ -21,28 +19,77 @@ during the design process wich will lead to better choices welding economic and
 relibility concerns.
 
 We will conduct a probabilistic analysis of multiple algorithms and compare
-results to theoritical values. We will also consider the algoriths complexity
+results to theoretical values. We will also consider the algoriths complexity
 and performance, both in resource consumption and in box usage.
 
-
-
-
-
 \clearpage
 
 \section{Bin packing use cases}
 
+Before studying the mathematics behind bin packing algorithms, we will have a
+look at the motivations behind this project.
 
-\cite{hofri:1987}
+Bin packing has applications in many fields and allows to automize and optimize
+complex systems. We will illustrate with examples focusing on two use cases:
+logistics and computer science. We will consider examples of multiple dimensions
+to show the versatility of bin packing algorithms.
 
+\paragraph{} In the modern day, an effective supply chain relies on an automated production
+thanks to sensors and actuators installed along conveyor belts. It is often
+required to implement a packing procedure. All of this is controlled by a
+computer system running continuously.
 
+\subsection{3D : Containers}
 
-\subsection{Logistics}
+Storing items in containers can be a prime application of bin packing. These
+tree-dimensional objects of standardized size are used to transport goods.
+While the dimensions of the containers are predictable, those of the transported
+items are not. Storage is furthermore complicated by the fact that there can be
+a void between items, allowing to move around. Multiple types of items can also
+be stored in the same container.
+
+There are many ways to optimize the storage of items in containers. For
+example, by ensuring items are of an optimal standardized size or by storing a
+specific item in each container, both eliminating the randomness in item size.
+In these settings, it is easy to fill a container by assimilating them to
+rectangular blocks. However, when items come in pseudo-random dimensions, it is
+intuitive to start filling the container with larger items and then filling the
+remaining gaps with smaller items. As containers must be closed, in the event
+of an overflow, the remaining items must be stored in another container.
+
+\subsection{2D : Cutting stock problem}
+
+In industries such as woodworking bin packing algorithms are utilized to
+minimize material waste when cutting large planks into smaller pieces of
+desired sizes. Many tools use this two-dimensional cut process. For example, at
+the Fabric'INSA Fablab, the milling machine, laser cutter and many more are
+used to cut large planks of wood into smaller pieces for student projects. In
+this scenario, we try to organize the desired cuts in a way that minimizes the
+unusable excess wood.
+
+\begin{figure}[ht]
+	\centering
+	\includegraphics[width=0.65\linewidth]{graphics/fraiseuse.jpg}
+	\caption[]{Milling machine at the Fabric'INSA Fablab \footnotemark}
+	\label{fig:fraiseuse}
+\end{figure}
+\footnotetext{Photo courtesy of Inés Bafaluy}
+
+Managing the placement of items of complex shapes can be optimized by using
+by various algorithms minimizing the waste of material.
+
+\subsection{1D : Networking}
+
+on which humans
+have decreasing control.
+
+In this paper, we will focus on one-dimensional bin packing, where we try to
+store items of different heights in a linear container.
 
-\subsection{chepa}
 
 \section{Next Fit Bin Packing algorithm}
 
+\cite{hofri:1987}
 % TODO mettre de l'Histoire
 
 \section{Next Fit Dual Bin Packing algorithm}