Overview
This course provides the
student with an introduction and examples of the mathematical model for simple
linear programming problems. It also deals with the concept of the graphic
method for solving linear programming problems, including the solution area and
vertices. This course aims at developing the student's ability to find the
system of equations, the simplified method, arithmetic improvements (checks),
coupling, sensitivity analysis, finite variables, and correct programming.
Intended learning outcomes
By the end of
the course, the student should be able to:
1.Recognize the
components of a linear programming problem and vertices, and the graphical way
to represent them
2.Explain some
types and concepts of systems of linear equations
3. Define methods
for solving systems of linear equations
4. Explain some
concepts such as sensitivity analysis, discrete variables, parametric
programming, and limited parametric programming.
5. Explain and analyze
linear programming problem components and vertices
6. Deduce the
concepts of the standard formula, the change of fundamentals, the pivot, and
the possible basic solutions
7. Compare
methods for solving systems of linear equations
8. Explore some
basic concepts of sensitivity analysis, discrete variables, parametric
programming, and limited parametric programming.
9. Solve a number of exercises and problems
with more than one idea about linear programming problem components and
vertices
10.
Apply exercises and problems to the standard formula, changing the basics, the
pivot, and the basic possible solutions
11.
uses methods for solving systems of linear equations
12.
Provides solutions to new, different, and multiple problems such as sensitivity
analysis, discrete variables, parametric programming, and limited parametric
programming.
Teaching and learning methods
1.Practical and theoretical lectures
2.
Discussion and dialogue
3.
Brainstorming
4.Working
papers, case study
5.
presentations
6.
Videos and e-learning
7.
Use of software and computer applications such as (MATLAB, Geogebra, Geometer)
8.
Intensifying applications, solving problems, and linking ideas to reality and
life situations
Methods of assessments
1.Written exam (essay + objective) = 25
marks, or its assessment is left to the course instructor
2.
Short tests (written or oral), demonstration tasks, applications, exercises and
presentation = 15 marks or left to the course instructor
3.
Written final exam (essay + objective) = 60 marks
Course content:
|
Week
|
Scientific subject
|
Number
of Hours
|
Lecture
|
exercises
|
|
1-2
|
Introduction: Examples illustrating the
formulation of the mathematical model for linear programming issues.
|
6
|
Ö
|
Ö
|
|
3-4
|
Some basic concepts of linear
programming, linear programming problem components and vertices, and the
graphical method.
|
6
|
Ö
|
Ö
|
|
5
|
First
Midterm ( 2 hours)
|
|
5-6
|
Systems of equations, standard form,
changing of fundamentals, modulation, possible principal solutions,
preserving the initial possibility, class selection of the pivot.
|
4
|
Ö
|
Ö
|
|
7-8-9
|
The simplified method, the objective
function and the scheduler, finding an initial possible schedule, the
two-stage simplified method, limitations of the simplified method,
alternative optimal solutions, avoiding circularity.
|
9
|
Ö
|
Ö
|
|
10
|
Second
Midterm ( 2 hours)
|
|
10-11
|
Modified Arithmetic Method, Modified
Simplified Method, Multiplication Formula, Modified Pivot Column Selection,
Modified Pivot Row.
|
4
|
Ö
|
Ö
|
|
12-13
|
Conjugation
simplified conjugation method, conjugation problem, relaxed complement terms,
simplified conjugation method, its results, meaning of conjugate variables.
|
6
|
Ö
|
Ö
|
|
14
|
sensitivity analysis, discrete variables,
parametric programming, limited parametric programming
|
3
|
Ö
|
Ö
|
|
|
Final
Exam
|
|
|
Total
|
42
|
|
|
References
Operations research and
linear programming / Dr. Thana Rashid
Sadiq
