Курс: Linear Programming

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Linear Programming Open course

Сгъване на всички Разгъване на всички
Contributors: Nadia Brauner (UGA, Grenoble), Hadrien Cambazard (Grenoble-INP), Nicolas Catusse (Grenoble-INP), Aurélie Lagoutte (UCA, Clermont), Pierre Lemaire (Grenoble-INP)

Contact: Nadia Brauner
- 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).
- One idea, one story: He did not know it was impossible, so he did it Страница
  
  Преглеждане
LP modelling
L’objectif est d’apprendre à modéliser un problème décrit en langage naturel en un Programme Linéaire.
- 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 simple problem described in natural language
- Linear Programming Modelling (course and corrected exercices, in French) Урок
- 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 :
  
  vidéo Introduction et exercice introductif (12 minutes)
  
  vidéo exercice 1 (alliage) (9 minutes)
  
  vidéo exercice 2 (gestion d'un réseau d'eau) (12 minutes)
- I read the course Тест
  
  Получаване на оценка
- 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
  
  Преглеждане
- OPL User Guide 1: Modeling LP problems with OPL using Caseine editor Файл
  
  Преглеждане
- Play with the example of the user guide Virtual programming lab
  
  Получаване на оценка
- Short OPL Tutorial Файл
  
  Преглеждане
- Sand Box Virtual programming lab
- Un problème de modélisation (in french)
- Basic exercises with no special difficulty
- Cucumbers and onions (example from the course) Virtual programming lab
  
  Получаване на оценка
- Vegetables (example from the course) Virtual programming lab
  
  Получаване на оценка
- Usine chimique Virtual programming lab
  
  Получаване на оценка
- Wine production Страница
- German Wines - Vins allemands (solution available) Virtual programming lab
  
  Получаване на оценка
- Perfumes Virtual programming lab
  
  Получаване на оценка
- Advertising Страница
- Advertizing - Publicités (solution available) Virtual programming lab
  
  Получаване на оценка
- Exercises with additional concepts
- Dairy Products Virtual programming lab
  
  Получаване на оценка
- Airline - Compagnie aérienne Virtual programming lab
  
  Получаване на оценка
- Steel Virtual programming lab
  
  Получаване на оценка
- The difficulty is to find the correct variables
- Olive oil production Страница
- Apples (mélanges) Virtual programming lab
  
  Получаване на оценка
- Recyclage de plastique (mélanges) Virtual programming lab
  
  Получаване на оценка
- The teapot - Le pot de terre et la théière (flot) Virtual programming lab
  
  Получаване на оценка
- Separate models and data
- OPL User guide 2: Modeling LP problems with OPL with external data Файл
- Airline - Compagnie aérienne with external data Virtual programming lab
  
  Получаване на оценка
- Management of a water network Virtual programming lab
  
  Получаване на оценка
- Production of wines with external data Virtual programming lab
  
  Получаване на оценка
- Bill Of Materials Virtual programming lab
  
  Получаване на оценка
- Pour aller plus loin : un problème agricole (étude de cas, gestion des stocks) URL
LP solving
- One idea, one story: the simplex algorithm is in the top 10 Страница
  
  Преглеждане
- 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
- Transformation betweeen forms Тест
  
  Получаване на оценка
- Changing forms step by step Тест
- Linearization (exercises with correction) Страница
- Canonical and standard forms (exercises with corrections) Страница
- 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
- Graphical representation of Cucumbers and onions with Geogebra
  
  Получаване на оценка
- Towards a solution Тест
  
  Получаване на оценка
- 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
  
  Получаване на оценка
- Go further with bases ** Тест
  
  Получаване на оценка
- Know the notion of pivoting and neighbor basis
  
  Before pivoting, recognize the variables 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 : Un article du journal le Monde qui parle de l'algorithme du simplexe (pourquoi il fonctionne si bien en pratique) URL
- I read the course again (basis and simplex algorithm) Тест
  
  Получаване на оценка
- Let's pivot Тест
  
  Получаване на оценка
- Phase I * Тест
  
  Получаване на оценка
- "software without mathware is only footware"
  Philosophe contemporain inconnu
  
  Go further with linear Programming
- A CPLEX Example Virtual programming lab
- A song to understand simplex method (based on the tableau method) URL
- Understand the LP modelling evaluation system URL
Duality ☯
- One idea, one story: the physics of shortest paths to detect useless streets ! Страница
  
  Преглеждане
- OPL User Guide: Analyse the value of the dual variables
- Write the dual of a linear program
  
  Calculate the units of the dual variables
  
  Give an economical interpretation of the dual program and of the optimal values of the dual variables
- 5 minutes pour apprendre à écrire le dual d'un programme linéaire (in French) URL
  
  Преглеждане
- Dual program Virtual programming lab
  
  Получаване на оценка
- Vidéo (12 min): Interprétation économique du dual dans un cas simple URL
- Vitamins Virtual programming lab
  
  Получаване на оценка
- Vitamins (Q2) Virtual programming lab
  
  Получаване на оценка
- Cucumber and onions culture (again!) Virtual programming lab
  
  Получаване на оценка
- Wines (Q1) Virtual programming lab
  
  Получаване на оценка
- Wines (Q2) Virtual programming lab
  
  Получаване на оценка
- Know the weak duality theorem and its application to make a proof of optimality
  
  Know the strong duality theorem and understand its interest
  
  Apply the complementary slackness property to find the values of the dual variables
  
  Describe an optimality proof for a given basis
- Vidéo (12min): Une façon de comprendre la construction du dual Страница
- Le théorème des écarts complémentaires (in French) Урок
  
  Go through the activity to the end
- I read the Duality course Тест
  
  Получаване на оценка
- Application du théorème des écarts complémentaires Тест
  
  Получаване на оценка
- A transportation problem
- The primal Тест
  
  Получаване на оценка
- The dual Тест
  
  Получаване на оценка
- A lab for the primal Virtual programming lab
  
  Получаване на оценка
- A lab for the dual Virtual programming lab
  
  Получаване на оценка
- Dualité en théorie des jeux (in french) Урок
  
  Преглеждане Go through the activity to the end
Sensitivity analysis
- Understand the relation between the dual variable and the shadow price
  
  Understand why the value of the dual variable does not change when the second member of the constraint is changed in the primal as long as the basis remains the same
  
  Understand the meaning of the complementary slackness property on the example
  
  Be able to calculate the validity bounds of the value of a dual variable
- Discover Exel Solver Страница
  
  Преглеждане
- Sensitivity Analysis Тест
  
  Получаване на оценка Получаване на оценка за преминаване
- Sensitivity analysis training Тест
  
  Получаване на оценка
- A complete exercice Тест
  
  Получаване на оценка
Place for contributors
This section is dedicated to new contributions on linear programming. You can add ideas in the forum and activities or course documents below.
- "software without mathware is only footware"
  Philosophe contemporain inconnu
  Pour aller plus loin avec la programmation linéaire
- Ideas and contributions for linear programming Форум
- One idea, one story: the simplex algorithm is in the top 10 (doublon ?) Страница
  
  Преглеждане
- Collections collaborative d'exercices de programmation linéaires База данни

Представяне по теми

Linear Programming Open course

LP modelling

LP solving

Duality ☯

Sensitivity analysis

Place for contributors