Instructor: Metin Türkay
Office: ENG-205, x1586
E-Mail: mturkay@ku.edu.tr e-mail for the course: indr262faq@ku.edu.tr
Lectures:
Section 01: Mn&We 14:30-15:45 ENG-Z50
Section 02: Mn&We 16:00-17:15 ENG-Z50
PS:
A: Fr 16:00-17:15 ENG-120
B: Th 17:30-18:45 SNA-B152
C: We 17:30-18:45 CASE-B24
Lab:
A: Tu 17:30-18:45 SNA-B152
B: Mo 17:30-18:45 SNA-B152
C: Fr 08:30-09:45 SNA-B152
Office Hours: Mn&We 13:00-14:30, Tu 10:00-11:30
TAs:
Esma Bozgeyik (EB), ENG-212, indr262faq@ku.edu.tr
Soheil Derakhshan Nejad (SDN), ENG-212, indr262faq@ku.edu.tr
Sadra Shoarinejad (SS), ENG-212, indr262faq@ku.edu.tr
Emre Kaan Yılmaz (EKY), ENG-212, indr262faq@ku.edu.tr
Tugce Uzer (TU), ENG-212, indr262faq@ku.edu.tr
Hümeyra Akyüz (HA), ENG-212
Ezgi Kalemoglu (EK), ENG-212
Perinaz Alp (PA), ENG-212
Abdullah Izgi (AI), ENG-212
TA Office Hours:
EB: We 11:00-12:00
SDN: Th 14:00-15:00
SS: Th 16:00-17:00
EKY:
TU: We 08:30-10:00
HA: Fr 14:30-15:45
EK: Mo 16:30-17:30
PA:
AI: Tu 16:00-17:30
KOLT Tutor:
Humeyra Akyuz: Mo 10:00-11:15, We: 11:30-12:45, Fr: 10:00-11:15
Brief Description
This course is designed to expose students to the concepts of modeling and optimization. The course emphasizes setting up optimization models from problem description and solving linear programming problems using the simplex method. The role of duality and sensitivity analysis for linear programming problems are examined. The range of problems that can be modeled and solved as linear programming problems are illustrated in engineering and management with computer implementations.
Course Goals
The students are expected to acquire the following skills in this course:
– Develop a fundamental understanding of linear programming models,
– Able to develop a linear programming model from problem description,
– Apply the simplex method for solving linear programming problems,
– Apply the revised simplex method to solve linear programming problems,
– Express the dual of a linear programming problem and solve the resulting dual problem using the dual simplex method, interpret the results and obtain solution to the primal problem from the solution of the dual problem,
– Conduct sensitivity analysis for linear programming problems and interpret the results,
– Apply the Hungarian method for solving assignment problems,
– Apply the transportation simplex method to solve transportation problems,
– Demonstrate hands-on problem solving skills for linear programming problems using a Python and a variety of solvers.
Textbook
Hillier, F.S. and G.J. Lieberman, ‘Introduction to Operations Research’, 10th Ed., 2015, McGraw Hill, New York.
Computer Laboratory and Problem Sessions
This course has 4 credits and involves problems sessions and computer laboratory. The problem sessions cover basic problem solving skills and reinforce the material covered in the lectures. There may be quizzes related to homework questions during the problem sessions. The computer laboratory sessions cover basic skills in developing models and using solvers by using Python. You will apply these skills in the homework assignments.
Note: Failure to attend the PS and Computer Labs will result in an automatic F in the course. Students can miss at most 1 PS or Computer Labs in the semester with approved excuse.
Homework and Computer Exercises
Homework is assigned to expose students to exercise problems and understanding of the theory, and to evaluate their abilities and knowledge. Students should be prepared to spend considerable time for preparing homework. Students are expected to submit their homework before the due date and time. In addition, there are computer exercises for modeling and solution of mathematical programming problems. The aim of the computer exercises is to help students gain hands-on experience with state-of-the-art programming software, Python. The computer exercises must be submitted by the announced deadline. Each student is required to complete the computer exercises alone from start to end. Failing to submit homework and computer exercises on time will result in 25% grade reduction for each late day.
Exams
There are two midterm exams during the semester and a final exam at the end of the semester. Exams will be closed book and notes. No make-up exams will be given unless required by Koç University policies. Students who are eligible for a make-up exam due to official reasons must contact the instructor at least one week prior to the exam date. If you miss an exam due to unforeseen circumstances such as severe illness, death in the family, etc., you must submit a written and signed statement as soon as possible, stating why you were unable to take the exam, together with any supporting documentation such as a doctor’s medical report. Failure to comply with these instructions unconditionally leads to zero being awarded for the exam grade.
Course grade will be determined as follows:
Midterm I (March 7, 2020, 13:15-16:15, SNA-A52& SNA-B172, SNA-B173) (Sample Exams: 2004, 2012) | 25% |
Midterm II (April 16, 2020, 19:0-22:00, SNA-A21& SNA-A22) (Sample Exams: 2004, 2012) | 25% |
Homework, Computer Exercises and Quizzes | 10% |
Term Project | 5% |
Participation (3% for classes, 2% for PS&Lab) | 5% |
Final Exam (TBA) (Sample Exams: 2004, 2012) | 30% |
Course Outline
Date | Subject | Material |
Week 1 | Review of Basic Linear Algebra Matrices and Vectors Systems of Linear Equations | |
Week 1 | PS: Linear Algebra | |
Week 2 | Modeling Optimization Problems Defining the Problem Formulating a Mathematical Model | Chapter 1, 2 |
Week 2 | PS: Modeling Optimization Problems | |
Week 3 | Formulation of Linear Programming Problems Standard Form of Linear Programming Models Assumptions in Linear Programming Examples of Linear Programming Models | Chapter 3 |
Week 3 | Lab: Introduction to Python | |
Weeks 4+5 | Solving Linear Programming Problems: The Simplex Method Setting up the Simplex Method The Algebra of the Simplex Method The Simplex Method in Tabular Form | Chapter 4 |
Week 4 | PS: Simplex Method | |
Week 5 | Lab: Modeling LP problems in Python | |
Week 6 | Starting Solution and Convergence The Two-Phase Method The Big-M Method | |
Week 6 | PS: Starting Solutions | |
Week 7 | Mid-Term I (March 7, 2020, 13:15-16:15, SNA-A52& SNA-B172, SNA-B173) Mid Term I Exercise Set, Solutions | Sample Exams: 2004, 2012 |
Weeks 7+8 | The Theory of the Simplex Method Extreme Points Basic Feasible Solutions The Revised Simplex Method | Chapter 5 PPT |
Week 7 | PS: The Theory of the Simplex | |
Week 8 | Lab: Solving LPs in Python | |
Week 9 | Duality Theory The Essence of Duality Theory and Primal-Dual Relationships Economic Interpretation of Duality | Chapter 6 (sections 6.1 through 6.4) |
Week 9 | PS: Duality | |
Week 9 | Mid-Term II (April 16, 2020, 19:0-22:00, SNA-A21& SNA-A22) | Sample Exams: 2004, 2012 |
Weeks 10+11 | Sensitivity Analysis The Essence of Sensitivity Analysis Applying Sensitivity Analysis | Chapter 6 (sections 6.5 through 6.7) |
Week 10 | Lab: Solving LPs in Python | |
Week 11 | PS: Dual Simplex | |
Week 12+13 | The Dual Simplex Method Parametric Linear Programming The Upper Bound Technique | Chapter 7 |
Week 12 | Lab: Managing optimization projects in Python | |
Week 13 | PS: Sensitivity Analysis | |
Week 14 | Special Cases of Linear Programming Problems The Transportation Problem The Assignment Problem | Chapter 8 |
Week 14 | PS: Review | |
Final Exams | Final Exam (TBA) | Sample Exams: 2004, 2012 |
Note: Topics to be covered and grade percentages may be modified by the course instructor.
Koç University Official Statement on Academic Honesty
Attendance Policy
All students are required to attend classes and discussion sessions such as tutorials, labs and problem sessions. The course instructor will take attendance.
The students who fail to attend 1/3 of classes and discussion sessions may get an automatic F.
March 7, 2020 13:15
SNA-A52& SNA-B172, SNA-B173Mid Term I (Sample Exams: 2004, 2012)April 16, 2020SNA-A21& SNA-A22
Mid Term II (Sample Exams: 2004, 2012)
Week | Date | Time & Room | Subject |
1 | January 27-31, 2020 | A: Fr 16:00-17:15 ENG-120 B: Th 17:30-18:45 SNA-B152 C: We 17:30-18:45 CASE-B24 | PS: Linear Algebra |
2 | February 3-7, 2020 | A: Fr 16:00-17:15 ENG-120 B: Th 17:30-18:45 SNA-B152 C: We 17:30-18:45 CASE-B24 | PS: Modeling Optimization Problems |
3 | February 10-14, 2020 | A: Tu 17:30-18:45 SNA-B152 B: Mo 17:30-18:45 SNA-B152 C: Fr 08:30-09:45 SNA-B152 | Lab: Introduction to Python |
4 | February 17-21, 2020 | A: Fr 16:00-17:15 ENG-120 B: Th 17:30-18:45 SNA-B152 C: We 17:30-18:45 CASE-B24 | PS: Simplex Method |
5 | February 24-28, 2020 | A: Tu 17:30-18:45 SNA-B152 B: Mo 17:30-18:45 SNA-B152 C: Fr 08:30-09:45 SNA-B152 | Lab: Modeling LP problems in Python |
6 | March 2-6, 2020 | A: Fr 16:00-17:15 ENG-120 B: Th 17:30-18:45 SNA-B152 C: We 17:30-18:45 CASE-B24 | PS: Starting Solutions, big-M, 2-Phase |
7 | March 9-13, 2020 | A: Fr 16:00-15:15 ENG-120 B: Th 17:30-18:45 SNA-B152 C: We 17:30-18:45 CASE-B24 | PS: The Theory of the Simplex |
8 | March 16-20, 2020 | A: Tu 17:30-18:45 SNA-B152 B: Mo 17:30-18:45 SNA-B152 C: Fr 08:30-09:45 SNA-B152 | Lab: Solving LPs in Python |
9 | March 23-27, 2020 | A: Fr 16:00-17:15 ENG-120 B: Th 17:30-18:45 SNA-B152 C: We 17:30-18:45 CASE-B24 | PS: Duality |
10 | March 30-April 3, 2020 | A: Tu 17:30-18:45 SNA-B152 B: Mo 17:30-18:45 SNA-B152 C: Fr 08:30-09:45 SNA-B152 | Lab: Solving LPs in Python |
April 6-10, 2020 | SPRING BREAK | SPRING BREAK | |
11 | April 13-17, 2020 | A: Fr 16:00-17:15 ENG-120 B: Th 17:30-18:45 SNA-B152 C: We 17:30-18:45 CASE-B24 | PS: Dual Simplex |
12 | April 20-24, 2020 | A: Tu 17:30-18:45 SNA-B152 B: Mo 17:30-18:45 SNA-B152 C: Fr 08:30-09:45 SNA-B152 | Lab: Managing optimization projects in Python |
13 | April 27-May 1, 2020 | A: Fr 16:00-17:15 ENG-120 B: Th 17:30-18:45 SNA-B152 C: We 17:30-18:45 CASE-B24 | PS: Sensitivity Analysis |
14 | May 4-8, 2019 | A: Fr 16:00-17:15 ENG-120 B: Th 17:30-18:45 SNA-B152 C: We 17:30-18:45 CASE-B24 | PS: Review |
Failure to attend the PS and Computer Labs will result in an automatic F in the course. Students can miss at most 1 PS or Computer Lab in the semester with approved excuse.
Date Due | Assignment | Solutions | PS/Lab | Quiz |
January 31, 2020 | HW#1 | PS | ||
February 7, 2020 | HW#2 | PS | ||
February 17, 2020 | Problems 3.1-7, 3.1-9, 3.1-14 | Lab | ||
February 21, 2020 | Problems 3.2-4, 3.2-5, 3.3-2, 3.4-4, 3.4-5 | PS | ||
February 28, 2020 | Solve Problems 4.1-2, 4.1-6, 4.3-5, 4.4-3 | Lab | ||
March 6, 2020 | Solve Problems 4.4-5, 4.4-7, 4.4-8, 4.5-2 | PS | ||
March 7, 2020 | Mid Term I 13:15-16:15, SNA-A52& SNA-B172, SNA-B173 | Sample Exams: 2004, 2012 | ||
March 16, 2020 | Problems 4.6-2 (excluding part h), 4.6-5 (parts a and c only), 4.6-7 (excluding part h) | PS | ||
March 20, 2020 | Lab | |||
March 27, 2020 | PS | |||
April 3, 2020 | Lab | |||
April 17, 2020 | PS | |||
April 16, 2020 | Mid Term II 19:00-22:00, SNA-A21&SNA-A22 | Sample Exams: 2004, 2012 | ||
April 24, 2020 | Lab | |||
May 1, 2020 | PS | |||
May 8, 2019 | PS | |||
May 15, 2020 | Bonus Project: coding Revised Simplex including 2-phase method and graphical user interface for solving LP problems. You can code in Python, Java, C++, or C# | – | – | – |
May 20, 2020 | Term Project: form your project groups- max 3 students per group [Project1][Project2] | You must login to your Novell account before downloading the solutions. | You must login to your Novell account before downloading the solutions. |
Reading 1: Optimizasyon, Metin Türkay
Reading 2: George B. Dantzig: Operations research Icon, 2005, Operations research, vol. 53, 892-898
Midterm I (TBA) (Sample Exams: 2004, 2012)