FACULTY OF ENGINEERING

Department of Industrial Engineering

IE 356 | Course Introduction and Application Information

Course Name
Mathematical Programming Models in Engineering
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
IE 356
Fall/Spring
2
2
3
6

Prerequisites
  IE 252 To succeed (To get a grade of at least DD)
Course Language
English
Course Type
Service Course
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course -
Course Coordinator -
Course Lecturer(s) -
Assistant(s) -
Course Objectives The aim of this course is to teach students building mathematical models of reallife problems and to enable them solving the complex problems encountered in industry and business. Emphasis is on framing the issues, articulating modeling components logically and analyzing the resulting model. It is intended to provide students with a solid foundation in the principles of model building as well as the algorithmic and theoretical side of mathematical programming. Handson modeling is particularly emphasized through many applications from various subjects and fields. Since nothing can be practically done without the help of good software, we have selected GAMS (the general algebraic modeling system) as the main tool to be used during the course. To facilitate its use, a detailed description of how problems need to be stated and the possibilities of GAMS are given
Learning Outcomes The students who succeeded in this course;
  • will be able to construct linear, integer and nonlimear mathematical models for some problems faced in engineering and science
  • will be able to analyze these models using mathematical programming methodologies
  • will be able to use GAMS software for different problems
  • will be able to calculate optimal solutions of developed mathematical models using GAMS software
  • will be able to analyze solutions
Course Description The main subjects of the course are the transportation problems, production scheduling problem, diet problem, network flow problem, portfolio problem, the 01 knapsack problem, the academy problem and school timetable problem and some examples of nonlinear programming, some useful modeling tricks, elements of convex analysis and the language features of the GAMS Package and some examples using GAMS

 



Course Category

Core Courses
Major Area Courses
X
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 The Transportation Problem. A GAMS Code to Solve the Transportation Problem. The Production Scheduling Problem Lecture notes
2 The Diet Problem. A GAMS Code to Solve the Diet Problem Lecture notes
3 The Network Flow Problem. A GAMS Code to Solve the Network Flow Problem Lecture notes
4 The Portfolio Problem and a GAMS Code for Solving it. Lecture notes
5 MixedInteger Linear Programming. The 01 Knapsack Problem And an Input GAMS File to Solve This Problem. Lecture notes
6 Identifying Relevant Symptoms and an Input GAMS File to Solve This Problem Lecture notes
7 The Academy Problem and an Input GAMS File to Solve This Problem Lecture notes
8 School Timetable Problem and an Input GAMS File to Solve This Problem Lecture notes
9 Models of Discrete Location and an Input GAMS File to Solve This Problem Lecture notes
10 Nonlinear Programming. Some Geometrically Motivated Examples. The Postal Package Example. The Tent Example. The Surface Example. An Input GAMS File to Solve These Problems Lecture notes
11 Some useful modeling tricks Lecture notes
12 Understanding the Set of All Feasible Solutions. Lines, Planes, Hyperplanes Lecture notes
13 Linear Spaces. Basis and Dimensions of linear Vector Spaces Lecture notes
14 Convex sets. Polyhedral sets. Cones Lecture notes
15 Extreme Points. Extreme Directions Lecture notes
16 Review of the Semester  

 

Course Notes/Textbooks Building and Solving Mathematical Programming Models in Engineering and Science. Enrique Castillo, Antonio J. Conejo, Pablo Pedregal, Ricardo Garcia, Natalia Alguacil, John Wiley & Sons, Inc., 2002, ISBN 0471150436
Suggested Readings/Materials Model Building in Mathematical Programming, Fourth Edition, H. Paul Williams, John Wiley & Sons, Ltd., 2003, ISBN 0 471 99788

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
1
10
Presentation / Jury
1
10
Project
Seminar / Workshop
Oral Exams
Midterm
1
35
Final Exam
1
45
Total

Weighting of Semester Activities on the Final Grade
55
Weighting of End-of-Semester Activities on the Final Grade
45
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
15
4
60
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
4
5
20
Presentation / Jury
1
10
10
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
1
12
12
Final Exam
1
20
20
    Total
170

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have adequate knowledge in Mathematics, Science and Industrial Engineering; to be able to use theoretical and applied information in these areas to model and solve Industrial Engineering problems.

X
2

To be able to identify, formulate and solve complex Industrial Engineering problems by using state-of-the-art methods, techniques and equipment; to be able to select and apply proper analysis and modeling methods for this purpose.

X
3

To be able to analyze a complex system, process, device or product, and to design with realistic limitations to meet the requirements using modern design techniques.

X
4

To be able to choose and use the required modern techniques and tools for Industrial Engineering applications; to be able to use information technologies efficiently.

X
5

To be able to design and do simulation and/or experiment, collect and analyze data and interpret the results for investigating Industrial Engineering problems and Industrial Engineering related research areas.

X
6

To be able to work efficiently in Industrial Engineering disciplinary and multidisciplinary teams; to be able to work individually.

X
7

To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively; to be able to give and receive clear and comprehensible instructions

X
8

To have knowledge about contemporary issues and the global and societal effects of Industrial Engineering practices on health, environment, and safety; to be aware of the legal consequences of Industrial Engineering solutions.

X
9

To be aware of professional and ethical responsibility; to have knowledge of the standards used in Industrial Engineering practice.

X
10

To have knowledge about business life practices such as project management, risk management, and change management; to be aware of entrepreneurship and innovation; to have knowledge about sustainable development.

X
11

To be able to collect data in the area of Industrial Engineering; to be able to communicate with colleagues in a foreign language.

X
12

To be able to speak a second foreign at a medium level of fluency efficiently.

13

To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Industrial Engineering.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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