Corso: Linear Programming

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Linear Programming Open course

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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 Pagina
  
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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) Lezione
- 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 Quiz
  
  Ricevere una valutazione
- 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) File
  
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- OPL User Guide 1: Modeling LP problems with OPL using Caseine editor File
  
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- Play with the example of the user guide Virtual programming lab
  
  Ricevere una valutazione
- Short OPL Tutorial File
  
  Visualizzare
- 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
  
  Ricevere una valutazione
- Vegetables (example from the course) Virtual programming lab
  
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- Usine chimique Virtual programming lab
  
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- Wine production Pagina
- German Wines - Vins allemands (solution available) Virtual programming lab
  
  Ricevere una valutazione
- Perfumes Virtual programming lab
  
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- Advertising Pagina
- Advertizing - Publicités (solution available) Virtual programming lab
  
  Ricevere una valutazione
- Exercises with additional concepts
- Dairy Products Virtual programming lab
  
  Ricevere una valutazione
- Airline - Compagnie aérienne Virtual programming lab
  
  Ricevere una valutazione
- Steel Virtual programming lab
  
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- The difficulty is to find the correct variables
- Olive oil production Pagina
- Apples (mélanges) Virtual programming lab
  
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- Recyclage de plastique (mélanges) Virtual programming lab
  
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- The teapot - Le pot de terre et la théière (flot) Virtual programming lab
  
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- Separate models and data
- OPL User guide 2: Modeling LP problems with OPL with external data File
- Airline - Compagnie aérienne with external data Virtual programming lab
  
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- Management of a water network 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
LP solving
- One idea, one story: the simplex algorithm is in the top 10 Pagina
  
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- 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 Quiz
  
  Ricevere una valutazione
- Changing forms step by step Quiz
- Linearization (exercises with correction) Pagina
- Canonical and standard forms (exercises with corrections) Pagina
- 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
  
  Ricevere una valutazione
- Towards a solution Quiz
  
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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 Quiz
  
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- Go further with bases ** Quiz
  
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- 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) Quiz
  
  Ricevere una valutazione
- Let's pivot Quiz
  
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- Phase I * Quiz
  
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- "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 ! Pagina
  
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- 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
  
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- Dual program Virtual programming lab
  
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- Vidéo (12 min): Interprétation économique du dual dans un cas simple URL
- Vitamins Virtual programming lab
  
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- Vitamins (Q2) Virtual programming lab
  
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- Cucumber and onions culture (again!) Virtual programming lab
  
  Ricevere una valutazione
- Wines (Q1) Virtual programming lab
  
  Ricevere una valutazione
- Wines (Q2) Virtual programming lab
  
  Ricevere una valutazione
- 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 Pagina
- Le théorème des écarts complémentaires (in French) Lezione
  
  Raggiungere la fine dell'attività
- I read the Duality course Quiz
  
  Ricevere una valutazione
- Application du théorème des écarts complémentaires Quiz
  
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- A transportation problem
- The primal Quiz
  
  Ricevere una valutazione
- The dual Quiz
  
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- A lab for the primal Virtual programming lab
  
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- A lab for the dual Virtual programming lab
  
  Ricevere una valutazione
- Dualité en théorie des jeux (in french) Lezione
  
  Visualizzare Raggiungere la fine dell'attività
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 Pagina
  
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- Sensitivity Analysis Quiz
  
  Ricevere una valutazione Ottenere la sufficienza
- Sensitivity analysis training Quiz
  
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- A complete exercice Quiz
  
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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 Forum
- One idea, one story: the simplex algorithm is in the top 10 (doublon ?) Pagina
  
  Visualizzare
- Collections collaborative d'exercices de programmation linéaires Database

Indice degli argomenti

Linear Programming Open course

LP modelling

LP solving

Duality ☯

Sensitivity analysis

Place for contributors