Indr 363

Mathematical Programming





Instructor:           Metin Türkay                                         TAs: S. Boğ & U. Kaplan

Office:                 ENG-205                                                      ENG-Z08, ENG-210

Phone:                 1586                                                              1767, 2648

E-Mail:                                    ,

Classes:               Mo, We:  09:30-10:45, ENG-B30

Office Hours:       Mo, We: 11:00-12:00

Course Web Page:


Brief Description

This course is designed to expose students to the concepts of optimization models and solution methods that include integer variables and nonlinear constraints.  The topics covered include: introduction to modeling with integer variables and integer programming; dynamic programming; convexity and nonlinear optimization; applications of various optimization methods in manufacturing, product design, communications networks, transportation, supply chain, and financial systems.


Hillier, F.S. and G.J. Lieberman, “Introduction to Operations Research”, 8th Ed., 2005, McGraw Hill, New York.

Problem Sessions and Computer Laboratory

In order to facilitate the topics covered, this course includes problem sessions and computer laboratory.  The problem sessions are intended for strengthening basic problem solving skills and reinforcing the material covered in the lectures.  The computer laboratory sessions cover basic skills in developing models and solution algorithms for solving the type of problems covered in the lectures using a software platform, OPL Studio for integer programming problems and GAMS for nonlinear programming problems.

Classroom Participation

The involvement of the student in all class activities, including computer laboratory and problem sessions, is essential and will be graded.

Homework and Computer Exercises

Homework is assigned to expose students to more complex 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 some hands-on experience with state-of-the-art mathematical programming software, OPL Studio. The computer exercises must be submitted by the announced deadline.  Each student is required to develop the computer exercises alone from start to end.


Exams for this course are targeted at evaluating the performance of students.  So no form of information exchange during the exams will be permitted.  There will always be a reasonable time limit at the exams.  There are two Midterm exams during the semester and a Final exam at the end of the semester.

Final grades will be determined as follows:

Mid-Term I


Mid-Term II


Final Exam


Course Outline




September 26-September 28

Special Cases of the Simplex Method

The Transportation Problem

The Assignment Problem

Chapter 8


October 3-October 24

Network Optimization Models

The Shortest-Path Problem

The Minimum Spanning Tree Problem

The Maximum Flow Problem

The Minimum Cost Flow Problem

The Network Simplex Method

Chapter 9

Notes 1


October 26

Mid-Term I

 Sample Exam

November 14-November 23

Integer Programming

Integer Programming Models

Integer Programming Models with Binary Variables

The Branch-and-Bound Method for Solving Integer Programming Problems

Other Methods for Solving Integer Programming Problems

Chapter 12


November 28-December 6

Dynamic Programming

Introduction to Dynamic Programming Problems

Deterministic Dynamic Programming

Stochastic Dynamic Programming

Chapter 11


December 7

Mid-Term II

 Sample Exam

December 12-January 4

Nonlinear Programming

Introduction to Nonlinear Programming

Types of Nonlinear Programming Problems

Single-Variable Unconstrained Optimization

Multivariable Unconstrained Optimization

Constrained Optimization and the Karush-Kuhn-Tucker (KKT) Optimality Conditions

Special Cases of Nonlinear Programming Problems

Chapter 13


January 20 Final Sample Exam

Note: Topics to be covered and grade percentages may be modified by the course instructor.

Academic Honesty

Honesty and trust are important to all of us as individuals. Students and faculty adhere to the following principles of academic honesty at Koç University:

Individual accountability for all individual work, written or oral:  Copying from others or providing answers or information, written or oral, to others is cheating.

Providing proper acknowledgment of original author:  Copying from another student's paper or from another text without written acknowledgment is plagiarism.

Study or project group activity is effective and authorized teamwork:  Unauthorized help from another person or having someone else write one's paper or assignment is collusion.

Cheating, plagiarism, and collusion are serious offenses resulting in an F grade and disciplinary action.

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.

 Copyright Koç University and Metin Türkay