الحقيبة التدريبية: Fundamentals of Operations Research (2023-2024)

مخطط الموضوع

Description of the Course Structure

Course description card: Fundamentals of Operations Research

Coefficient

Credit

Weekly Course Hourly

Weekly Lectures

Hours

Weekly

Practice

Hours

3hrs

1.5 hrs

Course Unit: Methodological Unit

Information about the Course Committee

Prepared by: Dr. Lemya Mekarssi

Academic Qualification: Hbilitation

Assessment methods

Continuous Assessment:	final Exam
40%	60%

Students' Assessment Methods :

Guided Work: Based on the following points:

-Exercise series to evaluate the student on each axis.

- Homework (report or short research) prepared by the students to be submitted to the professor later.

-short Exams

- Discipline and participation.

Final Exam

Lecture exam at the end of the semester

Target Audience:

Second Year Bachelor Commercial Sciences

Prerequisites:

Basic knowledge of mathematics, especially linear algebra and matrices

Skills or knowledge acquired by the student after studying the course:

Upon completion of this course, students will be able to:

Understand the basic concepts of operations research

Apply operations research techniques to solve managerial problems

Use operations research techniques to make better decisions

Pedagogical objectives:

Provide the student with some of the techniques used by operations research (linear programming) to solve problems in the institution.

Course Description

Operations research (OR) is a field that uses mathematical and analytical methods to help organizations make better decisions. OR techniques are used in a wide variety of industries, including manufacturing, healthcare, finance, and logistics. This course introduces the fundamental concepts and techniques of operations research. Students will learn how to apply these techniques to solve real-world problems in a variety of industries.

Course Content:

Axis 1: general introduction to operations research.

Axis 2: Linear Programming

Axis 3: Linear programming: Graphical method.

Axis 4: linear programming: Simplex method.

Axis 5: Linear Programming: Duality.

Axis 6: Programming integers: Cutting Plane Method.

Axis 7: Transportation problems.

References:

Arabic Refferences

English Refferences

1. خالد زهدي مصطى خواجة، مدخل إلى بحوث العمليات والبرمجة الخطية، دار وائل للنشر والتوزيع، الأردن، 2022

2. طلال عبود، طاهر حسن، بحوث العمليات، منشورات الجامعة الافتراضية السورية، الجمهورية العربية السورية، 2021

3. عادل مستوي، مطبوعة دروس وتمارين تطبيقية في مقياس رياضيات المؤسسة، ، جامعة الجزائر 3، 2020/2021

4. يزيد مقراني، مطبوعة محاضرات وتطبيقات في بحوث العمليات 1، جامعة بومرداس، 2018/2019

5. رجال السعدي، بحوث العمليات: البرمجة الخطية، الطبعة الأولى، دار رجزو، قسنطينة، الجزائر، 2004.

6. إلهام يحياوي، مطبوعة محاضرات مقياس رياضيات المؤسسة، جامعة باتنة، دس.

7. فاتح لقوقي، مطبوعة في مقياس رياضيات المؤسسة: محاضرات مدعمة بأمثلة محلولة باستخدام برنامج QM، جامعة أم البواقي، دس.

1. Monika, Operations Research Techniques, Paper Code – 20MAT22C5, Maharshi Dayanand University Press, India, 2021.

2. N. H. Gaither and J. A. Frazier, Quantitative Techniques for Managers, 10^th edition,Cengage Learning, 2018.

3. Hamdu A. Taha, Operations Research: An Introduction, 10^th edition, Pearson Education, Malaysia, 2017.

4. Ge Yijiang& Ge Jiuyan, Introduction to Operations Research, Hohai University Press, 2011.

5. J K Sharma, Operations Research: Therory and Applications, 6^th edition, Trinity, India, 2008.

6. P. Rama Murthy, Operations Research, 2^nd edition, New Age International Publishers, New Delhi, 2007.

7. Y. İlker Topcu, Operations Research: Lecture Notes, Informs, 2005.

8. Wayne L. Winston, Operations Research: Applications and Algorithms, 4^th edition, Thomson Learning, Canada, 2004.

Axis 1: general introduction to operations research.
Axis 1: general introduction to operations research.

Operations research (OR) is a field that uses mathematical and analytical methods to help organizations make better decisions. OR techniques can be used to improve efficiency, reduce costs, and make better use of resources. OR is used in a wide variety of industries, including manufacturing, healthcare, finance, and logistics.
Axis Two: Linear Programming
Axis Two: Linear Programming

Linear programming is a mathematical technique used to optimize a linear objective function, subject to a set of linear constraints. It is one of the most widely used techniques in operations research, and has applications in a wide variety of fields, including manufacturing, finance, and logistics. Linear programming is a powerful tool that can be used to solve a wide variety of problems. It is often used to optimize resource allocation, scheduling, and production planning.
Axis Three: LP Graphical Method
Axis Three: LP Graphical Method

The graphical method is a technique used to solve linear programming problems involving two decision variables. It provides a visual representation of the feasible region, which is the set of points that satisfy all the constraints of the problem. The graphical method allows us to identify the optimal solution geometrically.
Axis Four: linear programming: Simplex method.
Axis Four: linear programming: Simplex method.

The simplex method is a pivotal algorithm in linear programming, renowned for its efficiency and widespread applications. It provides a systematic approach to identify the optimal solution to complex problems involving multiple constraints and decision variables. The method's iterative nature and ability to handle large-scale problems have made it an indispensable tool in operations research, resource allocation, production planning, and various other domains that require optimization
Axis Five: Linear Programming: Duality
Axis Five: Linear Programming: Duality

The concept of duality in linear programming is of profound significance as it establishes a strong connection between a primal problem and its associated dual problem. Duality theory provides valuable insights, facilitating the analysis of the original problem through its dual counterpart. It aids in determining the existence of solutions, deriving sensitivity information, and developing efficient algorithms for solving large-scale linear programming models.
Axis Six: Programming integers: Cutting Plane Method.
Axis Six: Programming integers: Cutting Plane Method.

The cutting plane method is a powerful technique for solving integer programming problems, which involve decision variables that must take integer values. It addresses the computational challenges posed by the discrete nature of such problems by iteratively adding linear inequalities (cutting planes) to tighten the feasible region and converge towards the optimal integer solution. This method finds widespread applications in areas like scheduling, networks, and combinatorial optimization, where integer constraints are prevalent.
Axis Seven: Transportation problems.
Axis Seven: Transportation problems.

Transportation problems are a crucial application area of linear programming, aimed at minimizing the total cost of shipping goods from multiple sources to various destinations. These problems arise frequently in logistics, supply chain management, and distribution networks. Solving transportation problems using linear programming techniques enables companies to optimize their transportation plans, reduce costs, and improve overall operational efficiency.
Exercises
Exercises

This section includes a series of exercises with solutions on the lectures that have been addressed in the Operations Research Course.
Models of Exams
Models of Exams

This section includes models of previous exams with their typical solutions
- Exam+Solution 2022 ملف
- OR Final Exam ملف

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