Category of courses dedicated to OR 

Operations Research offers scientific methods for better decisions. The idea is to develop and use mathematics and informatics tools to solve complex organization problems. Historical applications are in the management of large systems of humans, machines, materials in industry, service, humanitarian aid, environment... 

At the end of this course, students should be able to propose a modelization and implement practical solutions (dedicated or industrial tools) to solve a decision or optimization problem. 

Skills 

•  Recognize a situation where Operations Research is relevant.
• Know the main tools of Operations Research.
• Have the methodological elements to choose the solution methods and the tools the most adapted for a given practical problem.
• Know how to manipulate the software tools to solve a discrete optimization problem.

The course covers various topics:

• Linear Programming (modelling, solving, duality)
• Mixed Integer Linear Programming (modelling techniques, solving with Branch and Bound)
• Dynamic Programming
• Bonus (riddles, elsewhere on the web, OR News)

Modelling and linear programming :
- Linear Programming (LP): LP model, Simplex algorithm, Duality, Sensitivity analysis.
Construction of a LP model: variables with constraints and objective function, optimum, unbounded variables,
networks and flow structures ...
- Production planning (labworks) : Microsoft Excel solver.

The course covers various topics:
• Integer Linear Programming
• Dynamic Programming
• Graph Theory
• Models for problems encountered in production planning and logistic

Content of the course:

Methods:

  • Material Requirement Planning
  • Mixted integer programming: Modeling, branch and bound, linear relaxation, quality of formulation

Application's domain:

  • Production Planning
  • Picking 
  • Timetabling

Objectives of course:

Expected skills:

  • General understanding of the planning tasks along the supply chain.
  • General knowledge about the key problems encountered in various contexts of operations management: production planning, picking in warehouses, transport planning, timetabling
  • Being able to model some classical problems in production and operations management.

Knowing, understanding and knowing how to apply the methods:

  • Mixed Integer Linear Programming (assuming your know Linear Programming)
  • MRP methods
  • Modeling using graph theory

Constraint Programming (CP) is a modeling and solving framework in combinatorial optimization. This course presents the fundamental ideas of CP and its application to scheduling. In particular, the course will go through:

  • Local consistencies as properties of the domains: arc-consistency and bounds-consistency
  • Local consistencies as algorithms: filtering algorithms of global constraints such as Linear (in)equation, AllDifferent, NoOverlap 
  • Modeling with typical constraints (Element, AllDifferent, Global Cardinality, NoOverlap, Cumulative...) and first insights about symmetry breaking and redundant constraints
  • Basic knowledge of tree search, backtracking algorithms and branching heuristics

The course builds upon fundamental techniques of Operations Research such as dynamic programming and graph theory (flow and matching).

Online modeling exercises and quiz have to be completed with a commercial or open-source CP solver to gain a strong and practical modeling skill in CP.

Note: the Caseine course is not (yet) self-contained and is tightly linked to 12h of class sessions and 4h30 of practical sessions

Cours de méthodes quantitatives (optimisation, programmation linéaire) pour la production et la logistique. Ce cours sert de «remise à niveau» pour les étudiants de l'IAE Grenoble venant à GI dans le cadre d'un double diplôme.


Très simples à décrire, les graphes sont des outils très puissants de modélisation de problèmes. L’objectif de ce cours est de reconnaitre différents problèmes d'optimisation et d’associer à chacun d'eux une méthode de résolution. Pour ce faire, les outils nécessaires au développement, à la compréhension et à la description des principales méthodes d’optimisation en théorie des graphes sont décrits. Les principaux algorithmes de théorie des graphes sont prouvés (description, analyse de complexité, preuve qu’il répond à la question posée) et implémentés avec les structures de données adéquates.

Le cours couvre les sujets suivants :
  • Notions de base et avancées sur les graphes 
  • Cheminement 
  • Arbres 
  • Plus courts chemins 
  • Coloration 
  • Couplage

Vous allez pénétrer en Graphistan. Vos connaissances en graphe, en modélisation, en optimisation seront mises à rude épreuve. Sauron, Voldemort et Palpatine guettent le moindre faux pas. Qu'Euler soit avec vous !

Ce jeu de piste est ouvert à toute personne qui possède un compte sur Caseine...