56 lines
1.9 KiB
TeX
56 lines
1.9 KiB
TeX
\sectionnn{Introduction}
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Bin packing is the process of packing a set of items of different sizes into
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containers of a fixed capacity in a way that minimizes the number of containers
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used. This has applications in many fields, such as logistics, where we want to
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optimize the storage and transport of items in boxes, containers, trucks, etc. In
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this paper, we will focus on one-dimensional bin packing, where we try to store
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items of different heights in a linear container.
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Building mathematical models for bin packing is useful in understanding the
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problem and in designing better algorithms, depending on the use case. An
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algorithm optimized for packing cubes into boxes will not perform as well as
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another algorithm for packing long items into trucks. Studying the mathematics
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behind algorithms provides us with a better understanding of what works best.
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When operating at scale, every small detail can have a huge impact on overall
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efficiency and cost. Therefore, carefully developing algorithms based on solid
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mathematical models is crucial. As we have seen in our Automatics class, a
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small logic breach can be an issue in the long run in systems that are supposed
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to run autonomously. This situation can be avoided by using mathematical models
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during the design process wich will lead to better choices welding economic and
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relibility concerns.
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We will conduct a probabilistic analysis of multiple algorithms and compare
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results to theoritical values. We will also consider the algoriths complexity
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and performance, both in resource consumption and in box usage.
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\clearpage
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\section{Bin packing use cases}
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\subsection{Logistics}
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\subsection{chepa}
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\section{Next Fit Bin Packing algorithm}
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% TODO mettre de l'Histoire
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\section{Next Fit Dual Bin Packing algorithm}
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\section{Algorithm comparisons and optimization}
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\subsection{NFBP vs NFDBP}
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\subsection{Optimal algorithm}
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\sectionnn{Conclusion}
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