Course Description: Introduction to deterministic models of operations research including linear programming formulations, the simplex algorithm, degeneracy, geometry of convex polyhedra, duality theory, and sensitivity analysis. Special linear programming models for assignment, transportation, and network problems. Integer programming formulations along with branch and bound solution. Dynamic programming.

Course Outline: This course is mainly concerned with linear programming and some of its extensions. It will follow the first eight chapters and chapter 10 of the text Ecker and Kupferschmid.

1. Linear programming models and applications (1 week)
2. The simplex algorithm (3 weeks)
3. Geometry of the simplex algorithm (1 week)
4. Duality in linear programming (2 weeks)
5. Sensitivity analysis (1 week)
6. Network flow models (1 week)
7. Integer programming (1 week)
8. Interior point methods for linear programming (1 week)
9. Dynamic programming (2 weeks)

Homework: Approximately every two weeks. Homework and exam solutions will be available online. You may discuss the homeworks with other students. Homeworks will not be graded. Solving the homework problems (and other problems from the text) will improve your understanding of the material.

Exams: Three in-class exams during the semester. There will be no final exam. Each exam will include at least one question from the homeworks. You may bring one page of handwritten notes to each exam. The first exam will cover models and the simplex algorithm. The second exam will cover duality, sensitivity analysis, and network flow models. The third exam will cover integer programming, interior point methods, and dynamic programming. As you would expect, the exams must be all your own work.

Project: I will assign a project. This will involve modeling a problem and then analyzing the model. You may work in groups of up to three people for the project. You should use a computer package for the project — preferably AMPL. I will describe AMPL in more detail in a class.

Grades: 70% for the exams, 30% for the project.
The 70% for the exams is broken down as 10% for your worst exam and 30% for each of your best two exams.

For the purposes of Mid-Term Assessment, exam scores will be posted online, with identifying data removed.

Textbooks: These will be placed on reserve.
J. G. Ecker and M. Kupferschmid; Introduction to Operations Research (Reprinted by Krieger, 2004). Required.
Fourer, Gay, and Kernighan; AMPL: A Modeling Language for Mathematical Programming. The Scientific Press, Second Edition, 2002. This is the handbook for AMPL and is used for the project. Strongly recommended — you may be able to get away without buying the book, but having it available will make the project a lot easier. The first chapter of this book is available online.
In previous years, I’ve used the text R. L. Rardin; Optimization in Operations Research. Prentice-Hall, 1998.

The World Wide Web: This outline, the homeworks, the project, and information about AMPL will be available via my homepage,

Office hours: Tuesday: 1:00–3:00pm., or by appointment.

Cell phones: Cell phones must not disturb the class. Please ensure the ringer is turned off.

Student learning outcomes: An understanding of the mathematical underpinnings of linear programming. An ability to apply knowledge of mathematics, science and engineering. An ability to design and conduct experiments, as well as to analyze and interpret data. An ability to identify, formulate and solve engineering problems.

Academic integrity: Student-teacher relationships are based on mutual trust. Acts which violate this trust undermine the educational process. The Rensselaer Handbook defines various forms of academic dishonesty and procedures for responding to them. The penalties for cheating can include failure in the course, as well as harsher punishments.

Appealing grades: As with any other administrative question regarding this course, see me in the first instance. If we are unable to reach agreement, you may appeal my decision to Professor Drew.