Deterministic and dynamic models

Teacher(s)

Chevalier Philippe; De wolf Daniel (compensates Chevalier Philippe); Van Vyve Mathieu;

Language

French

Prerequisites

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.

Main themes

The teaching emphasizes the mathematical and algorithmic modeling approach, and the resolution of applications or problems in management sciences using mathematical methods or formal logic. It aims to develop a systematic approach to analysis and resolution:  What is the question in quantitative terms, which model correctly represents the question asked? What are the useful tools? Are the conditions of application respected? How to implement these tools, what is the solution of the model? What is the answer to the initial question in the context of the initial question, not in the universe of its mathematical or logical abstraction?

Learning outcomes

At the end of this learning unit, the student is able to :

The main objectives and aims of the course are: Learning how to formulate, solve and analyze the results of a mathematical model to solve a problem related to economic organizational, and technical systems under constraints.  The focus here is primarily on deterministic problems with known parameters and logical or algorithmic models.   Learning formalized and rigorous reasoning (which is more difficult to achieve and is aimed more at mathematical modeling "know-how") The development of the student's autonomy in the work and in the learning process. This course is applied to mathematical formalization in social sciences in general, with a particular focus on management applications. It aims to prepare students for the study of advanced quantitative models or "state of the art" analysis and decision support in the various fields of management

Content

1. Optimisation without constraints
2. Optimisation subject to constraints
3. Non-linear programming
4. Linear programming
5. Dynamic programming (recursion)

Teaching methods

The course is given in the form of
- lectures (the teacher defines the concepts, demonstrates the results, and illustrates them with the help of an application),
- exercise sessions (the teacher submits applications/problems to the students and proposes a solution approach)
- work on a project-case to be solved in a group.
Some lectures can be given via self-study video capsules followed by a question-and-answer session and exemplary exercises.

Evaluation methods

Final written exam consisting exclusively of exercises in the application of the material.
Active participation in exercise sessions
Group work consisting of the resolution of a case using a optimization software, this case is taken into account for the final evaluation for 25% of the mark in the first session. It is not considered in the second session.
The use of AI is strictly prohibited to generate the project code, solution, or report.

Other information

The group case study is only organized during the semester, it will not be possible to realize this case study during the summer session. Thus, a written exam counts for 100% of the grade in the second session.

Online resources

Course presentations, slides, exercise questions and examples of exam questions are available at the associated Moodle site.

Bibliography

Ronald Rardin, Optimization in Operations Research, Prentice Hall, 2014.
Selected papers on applications on Moodle.

Faculty or entity

> ESPO