Схема на раздела

    • Slides on Linear Programming Файл
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    • Transparents sur la programmation linéaire Файл
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    • LP Modelling

      L’objectif est d’apprendre à modéliser un problème décrit en langage naturel en un Programme Linéaire.
    • Parcours Modélisation PL (lien) URL
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    • Skills Modelling

      Know the definitions associated to LP: feasible solution, optimal solution, feasible region…

      Know the elements that form an LP: decision variables, objective function, constraints

      Be able to model an LP from a problem described in natural language

    • Linear Programming Modelling (course) Урок
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    • La programmation linéaire propose un cadre de modélisation pour des problèmes d'optimisation sous contraintes et des outils pour trouver des solutions optimales. Cet outil fondamental de la recherche opérationnelle a émergé lors de la seconde guerre mondiale.

      Cette leçon présente ce qu'est la programmation linéaire, un exemple de modélisation (concombre et oignons), les différentes représentations d'un programme linéaire et le vocabulaire associé.

      Une série de 3 vidéos présente comment modéliser un problème décrit en langage naturel en programme linéaire et 3 exemples types :

    • I read the course Тест
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    • Ressources pour les activités de modélisation auto-évaluées

    • The modeling labs allow you to practice modeling. Feel free to do as many as you can. The first step before doing a modeling lab is to write the model on paper to separate the difficulty of modeling from possible technical or syntax problems.

      The labs are written in IBM's OPL (Optimization Programming Language). The OPL User Guide 1 image describes an example of a linear program in OPL with the necessary syntax as well as how to write a model in a modeling lab. The Playing with the Example lab of the OPL User Guide 1 allows you to manipulate your first pre-filled OPL lab. The Short OPL Tutorial manual allows you to learn more about the OPL modeling language. You can model and solve your own PL problems in the Sandbox.
    • Mode d'emploi d'une activité de modélisation (in french) Файл
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    • OPL User Guide 1: Modeling LP problems with OPL using Caseine editor Файл
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    • Vous devez être inscrit dans le cours pour avoir accès à l'éditeur des exercices de programmation (une fois connecté, si vous voyez encore ce message, utilisez la roue dentée en haut à droite).

    • Play with the example of the user guide Virtual programming lab
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    • Short OPL Tutorial Файл
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    • Sand Box Virtual programming lab

    • Training (a modelling problem)

    • Basic exercises with no special difficulty

    • Cucumbers and onions (example from the course) Virtual programming lab
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    • Wine production (with correction) Страница
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    • German Wines Virtual programming lab
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    • Perfumes Virtual programming lab
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    • Advertising (with correction) Страница
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    • Exercises with additional concepts

    • Dairy Products Virtual programming lab
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    • The difficulty is to find the correct variables

    • Olive oil production (with correction) Страница
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    • Apples Virtual programming lab
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    • Plastic waste recycling - Recyclage de plastique Virtual programming lab
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    • Separate models and data

    • OPL User guide: Modeling LP problems with OPL with external data

    • Data Reconciliation for Material Flow Analysis Virtual programming lab
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    • Production of wines with external data Virtual programming lab
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    • Bill Of Materials Virtual programming lab
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    • Pour aller plus loin : un problème agricole (étude de cas, gestion des stocks) URL
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    • LP Solving

    • Parcours LP Solving URL

    • Skills Solving

      Recognize the canonical and standard forms and know the transformations

      Linearize an objective function of the form maximum of a minimum or minimum of a maximum

    • Playing with forms Тест
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    • Forms step by step Тест
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    • Canonical and standard forms (exercises with corrections) Страница
    • Linearization (exercises with correction) Страница
    • One idea, one story : Un article du journal le Monde qui parle de l'algorithme du simplexe (pourquoi il fonctionne si bien en pratique) URL

    • Solve graphically an LP with two variables:

      • draw the feasible region
      • draw the level lines for the objective function
      • find the optimal solution(s) on the graphic
    • Draw LPs in 2D with Geogebra
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    • Représentation 2D d'un problème très simple GeoGebra
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    • Graphical representation of Cucumbers and onions with Geogebra
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    • Towards a solution Тест
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    • Know the definition of a basis, a basic and a non-basic variable a basic solution and a feasible basic solution

      Make the connection between the graphical representation and the basic solutions (find the point corresponding to a basic solution and conversely)

      Know the relation between the extreme points of the feasible region and the feasible basic solutions

    • Bases Тест
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    • Go further with bases Тест
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    • One idea, one story: the simplex algorithm is in the top 10 Страница
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    • Corrections of the exercises on the basis Файл

    • Know the notion of pivoting and neighbor basis

      Before pivoting, recognize the variable that can enter the basis in order to improve the current solution

      While pivoting, know which variable can leave the basis

      Master the pivoting algorithm and be able to interpret it graphically

    • One idea, one story: Dantzig describes the origins of linear programming Файл
    • I read the course again Тест
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    • Let's pivot Тест
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    • Correction of Exercice 10 by Ernest Foussard Файл
    • Avez-vous bien compris l'algorithme du simplexe ? (avec vidéo) Тест
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    • Phase I Тест
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    • One idea, one story: He did not know it was impossible, so he did it Страница
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    • "All models are wrong, but some are useful"
      Attributed to Georges E. P. Box
      Go further with Linear Programming
    • A CPLEX Example Virtual programming lab
    • Understand the LP modelling evaluation system URL