مخطط الموضوع
Presentation of the subject:
Subject: Linear programming
Teaching Unit: UEM51 (O/P)
Field/Branch/Specialization: Information Systems
Credit: 04 Coefficient: 02.
Weekly teaching hours:- Materials (number of hours per week): 1.5 hours
- Tutorials (number of hours per week): 1.5 hours
Specialty: Information systems
Course objective: To raise students' awareness of the practical importance of linear optimization problems and enable them to master the underlying theoretical concepts and apply these techniques to practical problems.
Teacher responsible for the subject : GUETTICHE Mourad
Contact : Tel 0658559139 Email m.guettiche@centre-univ-mila.dz
Subject : linear Programming
Teaching Unit : UEM51 (O/P)
Field/ the branch/Specialization: Information Systems
Credit : 04 Coefficient : 02.
Weekly teaching hours:
- Materials (number of hours per week): 1.5 hours
- Tutorials (number of hours per week): 1.5 hours
Chapter 1 (Problem modelling)
The objective of this chapter is to introduce the basic concepts of linear programming, following this outline:
- Definition of a linear programme.
- Real-world problems modelling using linear programming (LP)
- Graphical solution of a LP
- Extracting the characteristics of the solution.
- Limitations of the graphical method.
Chapitre 2
The course aims to help students understand how the simplex algorithm works by providing simple, educational examples that highlight the following points:
- The standard form of a LP.
- The simplex algorithm
- Progression of the algorithm using the algebraic method and the practical method (tables).
Initialisation of the simplex algorithm
In Chapter 2, we studied the simplex method, which allows us to determine the optimal solution to a linear programme, moving from one feasible basic solution to another that improves the value of the objective function, starting with an initial solution.
However, the initial solution is not always obvious; sometimes an entire initialisation phase must be carried out.
For the initialisation of the simplex algorithm, i.e. finding a starting solution, two methods will be studied in this chapter.
- The two-phase method.
- The Big-M method.
Duality in lineare programming
In this chapter, we will study how, starting from a given linear program (called the primal program), we can construct another linear program called the dual program. The solution to the primal program is determined from the dual program and vice versa, based on duality theorems. In addition, the economic interpretation of dual variables allows us to determine the increase in revenue that would result from the use of additional units of one of the goods.
Références bibliographiques
1) Les technique de la recherché opérationnelle (Algorithme du simplexe), cours et exercices corrigés, les mathématiques à l’université, 2001.
2) ROSEAUX, « Exercices et problèmes résolus de la recherche opérationnelle, Masson 1998.