Operations Research for Logistics - 4GUL0209

Goal(s)

The course is taught in French (some e-learning activities are in English).

Acquire skills in integer linear programming, dynamic programming and graph theory to model and solve complex logistics problems.

Three expectations:

1- Knowing the tools: Knowing the objects handled (mastering the terminology of linear programming, dynamic programming and graphs, knowing how to use the right vocabulary in describing a problem and solving it);

2- Know how to apply the tools: know and know how to carry out simple reasoning (provide proofs for linear programming and graphs, know how to propose recurrence formulas for dynamic programming), and know and know how to carry out basic graph algorithms (basic linear programming algorithms are expected to be mastered, see Prerequisites);

3- Identify the right tools to solve concrete problems: Model concrete problems using the tools seen in class, and deduce the algorithm(s) needed to solve the problem.

Content(s)

The course follows the principle of reverse pedagogy. It therefore requires a high degree of autonomy and personal organization. Working together in a small team (3 to 5 students) enables students to exchange and share their knowledge, which in turn leads to better progress and more solid learning.

The course is organized around :

• Learning sequences (validation of expectations 1 and 2) :
  - Independent reading (CM for PLNE);
  - Application and modeling exercises to be prepared and Caseine activities to be carried out before the TD;
  - A review with the TD teacher, who will answer any questions and clarify any points that have caused difficulties;
  - An assessment to validate the sequence.

• Case studies (in groups of 3 to 4 students) (validation of expectations 1, 2 and 3):
  - Model the problem posed;
  - Solve the problem using the tools provided (Python, PL solver);
  - Write a synthesis;
  - Oral presentation of results.

• Final exam (validation of expectations 1, 2 and 3):

Contents

Content of the eight learning sequences :

• Session 1: Graph theory: basic concepts;
• Seq. 2a: Chain, cycle, path, circuit;
• Seq. 2b: Minimum-weight spanning trees;
• Seq. 3: Shortest path;
• Session 4: Dynamic programming;
• Seq. 5: Maximum flow and minimum cost flow;
• Seq. 6: Integer linear programming;
• Seq. 7: Modeling concrete problems.

Content of the case studies :

• Case Study 1: Dynamic Programming - modeling and solving a problem (Python programming language);
• Case Study 2: Integer Linear Programming - modeling and solving a problem (OPL - Cplex).

The course requires knowledge of :
- Linear programming: Linear Programming modeling, simplex algorithm, duality, economic interpretation (see description of UE Mathématiques et informatique décisionnelles - 3GUC0905)
- Algorithms and programming: basic notions of algorithms and mastery of a high-level programming language (e.g. Python) (see description of UE Modélisation mathématique et informatique

• 3GUC0205 and UE Mathématiques et informatique décisionnelles - 3GUC0905).