Feat: Étape 1 sur la binomiale
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\usepackage{myXsim}
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\usepackage{myXsim}
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\author{Benjamin Bertrand}
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\author{Benjamin Bertrand}
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\title{Binomiale et echantillonnage - Cours}
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\title{Simulation de suréservation}
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\date{octobre 2020}
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\date{octobre 2020}
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\DeclareExerciseCollection{banque}
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\DeclareExerciseCollection{banque}
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\collectexercises{banque}
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\collectexercises{banque}
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\begin{exercise}[subtitle={<++>}, step={1}, origin={<++>}, topics={Binomiale et echantillonnage}, tags={Probabilité, Échantillonnage, Binomiale}]
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\begin{exercise}[subtitle={Surréservation}, step={1}, origin={Création}, topics={Binomiale et echantillonnage}, tags={Probabilité, Échantillonnage, Binomiale}]
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<++>
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Pour obtenir un taux de remplissage convenable, les compagnies aériennes vendent régulièrement plus de place que n'en comporte l'avion car il arrive que des personnes ne se présentent pas au décollage. Si un passagers a réservé mais qu'il n'y a plus de place dans l'avion, il faudra par contre le dédommager. C'est pour cela qu'il faut évaluer le risque de surréservation.
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On considère une ligne aérienne entre deux villes pour laquelle:
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\begin{multicols}{2}
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\begin{itemize}
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\item Tous les avions ont 50 places.
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\item 53 réservations sont vendues pour chaque vol (on supposera qu'elles sont toutes vendues)
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\item Chaque personne ayant réservé a 9 chance sur 10 de se présenter à l'embarquement ( donc 1 chance sur 10 de ne pas se présenter).
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\item Un billet vendu rapporte 100\euro. Un billet remboursé coûte 250\euro à la compagnie.
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\item Chaque personne ayant réservé une place se présente au non à l'embarquement indépendamment des autres personnes ayant réservé sur le même vol.
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\end{itemize}
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\end{multicols}
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\begin{center}
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\textbf{La compagnie prend elle un risque en vendant 53 places au lieu des 50 disponibles?}
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\end{center}
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Pour évaluer les risques liés à une surréservation, nous allons \textbf{simuler} avec le tableur plusieurs vols sur cette ligne.
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\begin{enumerate}
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\item On commence par simuler un vol où 53 places ont été vendues.
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\begin{minipage}{0.6\textwidth}
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Pour savoir si une personne se présente ou non à l'embarquement, nous utiliserons la commande \calc{=SI(ALEA()>0.9;0;1)}. Cette commande renvoie:
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\begin{itemize}
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\item 0 si le passager ne s'est pas présenté
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\item 1 s'il s'est présenté.
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\end{itemize}
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\begin{enumerate}
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\item Réaliser la simulation pour le premier vol
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\item Combien de personnes se sont-elles présentées à l'embarquement?
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\item Quelle formule peut-on rentrer en \texttt{B56} pour calculer ce nombre?
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\end{enumerate}
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\end{minipage}
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\begin{minipage}{0.4\textwidth}
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\includegraphics[scale=0.27]{./fig/vol1}
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\end{minipage}
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\item
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\begin{enumerate}
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\item Réaliser cette simulation pour 100 vols de cette ligne.
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\hspace{-2cm}
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\includegraphics[scale=0.17]{./fig/vol100}
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\item Quelle formule doit-on entrer en \texttt{CX56} pour calculer la moyenne du nombre de passager?
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\item Pensez vous que le risque de surréservation est grand?
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\end{enumerate}
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\item On veut maintenant évaluer le risque de surréservation. Pour savoir si un vol est en surréservation, on utilise la commande \calc{=SI(nbr_passagers > 50;1;0)} (avec \lstinline|nbr_passagers| à remplacer le nom de la case)
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\begin{enumerate}
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\item Compléter le tableau pour connaître les vols en surréservation.
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\hspace{-2cm}
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\includegraphics[scale=0.15]{./fig/vol100_overbooking}
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\item Quelle formule doit-on rentrer en \texttt{CX59} pour compter le nombre de vols en surréservation?
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\item Quelle formule doit-on entrer dans \texttt{CX61} pour calculer la fréquence des vols en surréservation?
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\end{enumerate}
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\item Répondre à la question initiale en vous basant sur les résultats de votre simulation.
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\end{enumerate}
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\end{exercise}
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\end{exercise}
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\begin{solution}
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<++>
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\end{solution}
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\collectexercisesstop{banque}
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\collectexercisesstop{banque}
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Complementaire/01_Binomiale_et_echantillonnage/fig/vol1.pdf
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After Width: | Height: | Size: 57 KiB |
Loading…
Reference in New Issue
Block a user