Topic: Mixed Integer Programming | Operations Research (UGA)

Topic outline

Mixed Integer Programming
- MIP Modelling
- Parcours Modélisation MIP (lien) URL
- Slides MIP (in English) File
- Slides MIP Modelling (in French) File
- MIP modelling exercises with corrections (22-23) File
- Know the main modelling techniques (Shadok)
- One idea, one story: meet the 1962 Procter and Gamble challenge ! Page
  
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- Techiques générales de modélisation Lesson
  
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  Cette leçon présente des techniques générales de modélisation en programmation linéaire en nombres entiers. Les exemples de modélisations (avec corrigés) sont les suivants. La bouteille de lait signifie qu'ils sont également proposés en atelier de modélisation (en lien sur la bouteille).
  
  Exercices d'application des techniques de modélisation
  
  Au charbon ! : mise en œuvre de divers techniques de modélisation
  
  Le journal : variables booléennes indicatrices de positivité
- OPL User Guide: modelling integer/boolean variables
- C'est le bouquet ! Virtual programming lab
  
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- Toy shop Virtual programming lab
  
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- Windscreens wipers Virtual programming lab
  
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- Coals Virtual programming lab
  
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- Cars Virtual programming lab
  
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- Separate the model and the data
- OPL User Guide: using .dat files with OPL and the Caseine editor
- Lot sizing (example) Virtual programming lab
  
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- Répartition équitable Virtual programming lab
  
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- Matrix Sum (Euler Problem 345) Virtual programming lab
  
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- Dyeing Plant Virtual programming lab
  
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- Entrepôt pour produits toxiques Virtual programming lab
  
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- Toys Virtual programming lab
  
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- Fire stations Virtual programming lab
- Positioning cyclo-logistics depots in Bordeaux Virtual programming lab
  
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- Positioning cyclo-logistics depots in Bordeaux (cont.) Virtual programming lab
  
  Not available unless: The activity Positioning cyclo-logistics depots in Bordeaux is marked complete
- Planification spaciale marine (avec corrections) URL
- Marine Spatial Planning (with corrections) Page
- Mutualization of physical infrastructures (with corrections) File
- Know the main combinatorial optimization problems and model them as an integer linear program: knapsack, bin packing, set covering, set partitionning, minimum cost flow, shortest path.
- One idea, one story: when the salesman started its travel Page
  
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- Classical Combinatorial Problems File
- Problèmes classiques d'optimisation combinatoire (in French) File
  Ce document présente des modélisations pour les problèmes classiques d'optimisation combinatoire :
  
  Sac-à-dos : piste verte
  
  Bin packing : piste rouge
  
  Couverture d'ensemble : piste bleue
  
  Flot de cout minimum : piste rouge
  
  Plus court chemin : cas particulier du précédent
- Bin packing Virtual programming lab
  
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- Independent Set (Stable) Virtual programming lab
  
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- Maximum Matching Virtual programming lab
  
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- Chromatic number Virtual programming lab
  
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- A la recherche des Exoplanètes URL
- MIP Solving
- Parcours MIP solving (lien) URL
- Skills Solving
  
  Know the definition of a linear relaxation
  
  Know the relation between the value of an optimal solution of the MIP and of the linear relaxation
  
  Be able to explain the principle of the Branch and Bound algorithm graphically (2 variables)
  
  Know which variable can be branched on and the branching conditions
  
  Know how to calculate the lower and upper bound during the execution of the algorithm
  
  Know the conditions that allow to cut a branch
- Branch and bound and Linear Relaxation
- Slides MIP solving (en anglais) File
- Slides MIP résolution (en français) File
- Vidéo (13min): Mise en oeuvre de l'algorithme de branch and bound Page
- Branch & Bound course test Quiz
  
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- Branch & bound training Quiz
  
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- Branch and Bound Training again Quiz
  
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- Exercice Branch and Bound sur le sac-à-dos corrigé File
- Comprendre couplage, transversal et 2-approximation du transversal avec la programmation linéaire en vidéos URL
- Formulation and cuts
- Formulation and cuts Book
- Formulations* Quiz
  
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- Bin packing (without cuts) Virtual programming lab

Topic outline

Mixed Integer Programming

MIP Modelling

MIP Solving