From dd8bc6aeed6fd0f8034d36ccc662218b1d2daba8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Fran=C3=A7ois=20Pelletier?= Date: Sat, 21 Apr 2018 01:45:07 -0400 Subject: [PATCH] =?UTF-8?q?fin=20de=20l'ajout=20de=20contenu=20au=20rappor?= =?UTF-8?q?t,=20d=C3=A9but=20des=20corrections=20orthographiques,=20rendu?= =?UTF-8?q?=20=C3=A0=20la=20section=20approches?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Rapport_de_session/Annexe1.tex | 35 +++++++++--------- Rapport_de_session/Annexe2.tex | 38 ++++++++++++++------ Rapport_de_session/Tables/statistiques.ods | Bin 0 -> 12126 bytes Rapport_de_session/approche.tex | 36 +++++++++---------- Rapport_de_session/bibliographie.bib | 5 ++- Rapport_de_session/description.tex | 22 ++++++------ Rapport_de_session/etapes.pdf | Bin 16703 -> 16697 bytes Rapport_de_session/experimentation.tex | 1 - Rapport_de_session/introduction.tex | 4 +-- Rapport_de_session/rapport_de_recherche.pdf | Bin 1341681 -> 1258698 bytes Rapport_de_session/rapport_de_recherche.tex | 3 +- 11 files changed, 78 insertions(+), 66 deletions(-) create mode 100644 Rapport_de_session/Tables/statistiques.ods diff --git a/Rapport_de_session/Annexe1.tex b/Rapport_de_session/Annexe1.tex index 30f377a..48a47ef 100644 --- a/Rapport_de_session/Annexe1.tex +++ b/Rapport_de_session/Annexe1.tex @@ -1,70 +1,69 @@ +\begin{landscape} \section*{Annexe 1 : Horaires initiales générées par le modèle} \label{sec:AnnexeHoraires} -\newgeometry{margin=2cm} -\begin{landscape} \begin{table}[ht] \centering - \includegraphics[width=24cm]{Tables/InitialSchedule1.png} + \includegraphics[width=25cm]{Tables/InitialSchedule1.png} \caption{Horaire initiale ayant un ratio employés temps plein / employés temps partiel de 0.11.} \label{fig:InitialSchedule1} \end{table} -\thispagestyle{empty} + \clearpage \begin{table}[ht] \centering - \includegraphics[width=24cm]{Tables/InitialSchedule2.png} + \includegraphics[width=25cm]{Tables/InitialSchedule2.png} \caption{Horaire initiale ayant un ratio employés temps plein / employés temps partiel de 0.17.} \label{fig:InitialSchedule2} \end{table} -\thispagestyle{empty} + \clearpage \begin{table}[ht] \centering - \includegraphics[width=24cm]{Tables/InitialSchedule3.png} + \includegraphics[width=25cm]{Tables/InitialSchedule3.png} \caption{Horaire initiale ayant un ratio employés temps plein / employés temps partiel de 0.22.} \label{fig:InitialSchedule3} \end{table} -\thispagestyle{empty} + \clearpage \begin{table}[ht] \centering - \includegraphics[width=24cm]{Tables/InitialSchedule4.png} + \includegraphics[width=25cm]{Tables/InitialSchedule4.png} \caption{Horaire initiale ayant un ratio employés temps plein / employés temps partiel de 0.28.} \label{fig:InitialSchedule4} \end{table} -\thispagestyle{empty} + \clearpage \begin{table}[ht] \centering - \includegraphics[width=24cm]{Tables/InitialSchedule5.png} + \includegraphics[width=25cm]{Tables/InitialSchedule5.png} \caption{Horaire initiale ayant un ratio employés temps plein / employés temps partiel de 0.33.} \label{fig:InitialSchedule5} \end{table} -\thispagestyle{empty} + \clearpage \begin{table}[ht] \centering - \includegraphics[width=24cm]{Tables/InitialSchedule6.png} + \includegraphics[width=25cm]{Tables/InitialSchedule6.png} \caption{Horaire initiale ayant un ratio employés temps plein / employés temps partiel de 0.39.} \label{fig:InitialSchedule6} \end{table} -\thispagestyle{empty} + \clearpage \begin{table}[ht] \centering - \includegraphics[width=24cm]{Tables/InitialSchedule7.png} + \includegraphics[width=25cm]{Tables/InitialSchedule7.png} \caption{Horaire initiale ayant un ratio employés temps plein / employés temps partiel de 0.44.} \label{fig:InitialSchedule7} \end{table} -\thispagestyle{empty} + \clearpage \begin{table}[ht] \centering - \includegraphics[width=24cm]{Tables/InitialSchedule8.png} + \includegraphics[width=25cm]{Tables/InitialSchedule8.png} \caption{Horaire initiale ayant un ratio employés temps plein / employés temps partiel de 0.50.} \label{fig:InitialSchedule8} \end{table} -\thispagestyle{empty} + \clearpage \end{landscape} %%% Local Variables: diff --git a/Rapport_de_session/Annexe2.tex b/Rapport_de_session/Annexe2.tex index c9efab0..869149a 100644 --- a/Rapport_de_session/Annexe2.tex +++ b/Rapport_de_session/Annexe2.tex @@ -1,16 +1,32 @@ -\section*{Annexe 2 : Pseudo-Code de l'algorithme de recouvrement des horaires} +\section*{Annexe 2 : Pseudocode de l'algorithme de recouvrement des horaires} \label{sec:AnnexePseudo} -\pagebreak -\begin{landscape} +\begin{algorithm} + \DontPrintSemicolon + \KwData{nbEmployees, maxBacktrack, nbRecoveryActions, alreadyPerformedMatrix=False, currentRecoveredSchedule, solutionFound=0} + \KwResult{currentRecoveredSchedule} + \While{$\neg$solutionFound $\wedge$ nbBacktrack $<$ maxBacktrack}{ + \If{nbAvailRecoveryActions $>$ 0}{ + Choose minimum cost recoveryAction\; + \For{Employee and Work period}{ + Perform recoveryAction on currentRecoveredSchedule\; + Mark recoveryAction as performed in alreadyPerformed matrix\; + nbRecoveryActions-1\; + } + } + \Else{ + Update currentRecoveredSchedule\; + nbBacktrack+1\; + } + \If{nbAvailRecoveryActions=0}{ + solutionFound=True\; + \If{nbBacktrack mod nbEmployees = 0}{ + initialize alreadyPerformedMatrix\; + } + } + } +\caption{Algorithme de recouvrement} +\end{algorithm} -\begin{figure}[ht] - \centering - \includegraphics[width=25cm]{Figures/psedoCodeRecouvrement.png} - \caption{Pseudo-Code de l'algorithme de recouvrement des horaires.} - \label{fig:PseudoRecouvrement} -\end{figure} - -\end{landscape} %%% Local Variables: %%% mode: latex %%% TeX-master: "rapport_de_recherche" diff --git a/Rapport_de_session/Tables/statistiques.ods b/Rapport_de_session/Tables/statistiques.ods new file mode 100644 index 0000000000000000000000000000000000000000..380e684d8998f7ab1153ecd4ea34c0531c559dde GIT binary patch literal 12126 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zT0ud<($r$J63aPjF-rpl0}xQiQ{VzK3=9p-jV7}>sMVXIOBtFPn*+^2Q*LNsh#_Wd zX^JLhXkun!gehibhAw7mXaEs2N4Uw*)X>NhU7?wwDTXCxMi$1CA36AQm~pA9y863u F0RZsj{*nLy diff --git a/Rapport_de_session/experimentation.tex b/Rapport_de_session/experimentation.tex index a281f5a..55c46b0 100644 --- a/Rapport_de_session/experimentation.tex +++ b/Rapport_de_session/experimentation.tex @@ -14,7 +14,6 @@ L'instance de base pour la comparaison des différents résultats correspond au \label{fig:ModelesProposes} \end{figure} - La première approche explorée est de construire un seul modèle de programmation par contraintes pour l'ensemble du problème. Ce modèle incluait les contraintes sur les horaires ainsi que celles pour tous les types d'employés dans un seul modèle. De plus, le nombre d'employé était aussi une variable qui était modélisée en utilisant la possibilité d'inclure un horaire n'ayant aucune période de travail. Cette approche a permis de confirmer que notre problème était satisfiable, mais qu'il était difficile d'obtenir une variété de solutions, ce qui était nécessaire pour la création des scénarios. Une fonction d'optimisation a aussi été proposée, mais la formulation du problème faisait en sorte qu'il est toujours plus efficace de maximiser le nombre d'employés à temps plein. Il a donc été choisi d'instancier le nombre d'employés de chaque type manuellement, de tester la satisfiabilité de l'instance dans chaque cas et ensuite de borner le nombre d'employés de chaque type. Ce choix est devenu notre seconde approche. diff --git a/Rapport_de_session/introduction.tex b/Rapport_de_session/introduction.tex index 09551a0..3cf4d0d 100644 --- a/Rapport_de_session/introduction.tex +++ b/Rapport_de_session/introduction.tex @@ -1,9 +1,9 @@ \section{Introduction} \label{sec:Introduction} -La planification d'horaires de travail est un enjeu important pour plusieurs industries et entités gouvernementales. Une mauvaise planification des ressources en fonction de la demande de travail d'une entreprise peut entraîner une diminution des profits en plus d'avoir des répercussions sur les dates de livraison de ses différents contrats. Parmi les raisons qui rendent cette tâche difficile, il y a les restrictions complexes provenant de la loi du travail, une variabilité de la demande de travail selon les période de l'année et une incertitude liée à l'absentéisme des employés. Il devient donc important de produire des horaires de travail permettant une flexibilité d'ajustement en fonction de la demande de travail et de l'absentéisme des employés, tout en minimisant le coût des salaires. +La planification d'horaires de travail est un enjeu important pour plusieurs entreprises et organisations publiques. Si elle est inadéquate, elle peut entrainer une diminution des profits en plus d'avoir des répercussions sur les dates de livraison de ses différents contrats. Parmi les raisons qui rendent cette tâche difficile, on dénombre les restrictions complexes de la loi sur les normes du travail, une variabilité saisonnière des besoins en main-d'oeuvre et une incertitude liée au taux d'absentéisme. Les horaires produits doivent permettre le rajustement selon les deux facteurs précédents, tout en minimisant le cout des salaires. -Le présent travail propose une approche stoechastique pour la génération d'horaires de travail robustes en fonction du taux d'absentéisme et du taux d'augmentation de la demande de travail. Une banque d'horaires valides est d'abord générée avec le solveur Choco de manière efficace et en prenant soin d'obtenir des horaires avec des différences importantes quant aux types d'employés (temps plein ou temps partiel) la caractérisant. Par la suite, ces différents horaires sont soumis à des simulations durant lesquelles sont générées des absences et des augmentations ponctuelles de la demande de travail. Un algorithme de recouvrement est ensuite utilisé pour combler les différentes plages horaires en déficit de main-d'oeuvre. Les coûts de recouvrement moyens de ces différents horaires modifiés serviront à évaluer la robustesse des horaires face aux probabilités d'absentéisme et d'augmentation de la demande. Enfin, des résultats montreront que cette méthode permet d'évaluer le ratio \texttt{employés temps plein / employés temps partiel} optimal en fonction des probabilités d'absentéisme et d'augmentation de la charge de travail. +Le présent rapport propose une approche stochastique pour la production d'horaires robustes en fonction du taux d'absentéisme et de la variabilité de la demande de travail. Une banque d'horaires valides est d'abord générée avec le solveur Choco de manière efficace et en prenant soin d'obtenir des différences importantes quant aux types d'employés (temps plein ou partiel). Par la suite, ces horaires variés sont soumis à une fonction qui génère des absences et des augmentations ponctuelles de la demande de travail. On utilise ensuite un algorithme de recouvrement pour combler les différentes périodes en déficit de main-d'{\oe}uvre. Les couts de recouvrement moyens de ces différents horaires modifiés serviront à évaluer la robustesse des horaires face aux probabilités d'absentéisme et d'augmentation de la demande. 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