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 seven chapters and section 21.1 of the text by Kupferschmid available on LMS.

• Linear programming models and applications (1 week)

• The simplex algorithm (3 weeks)

• Geometry of the simplex algorithm (1 week)

• Duality in linear programming (2 weeks)

• Sensitivity analysis (1 week)

• Network flow models (1 week)

• Integer programming (2 weeks)

• Dynamic programming (1 week)

• Interior point methods for linear programming (1 week)

Lectures: Lecture notes will be posted on LMS. Links to the recordings of the lectures themselves from 2020 will be provided from the course webpage and LMS.

Piazza: We’ll be conducting all class-related discussion on Piazza this term. The quicker you begin asking questions on Piazza (rather than via emails), the quicker you’ll benefit from the collective knowledge of your classmates and instructors. We encourage you to ask questions when you’re struggling to understand a concept. You can even do so anonymously. Link:

https://piazza.com/rpi/fall2023/matp4700

Homework: Approximately every week. Homework and exam solutions will be made available online after the due date. You may discuss the homeworks with other students. Solving the homework problems (and other problems from the text) will improve your understanding of the material. Working out the problems yourself will greatly improve your understanding of the material and help you on the exams.

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. Exam dates: Oct 3, Nov 7, Dec 8.

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. Other options for modeling languages are Pyomo and HiGHS. You will submit your work on the project on LMS. There will be 3 stages: initial formulation of a working optimization model, sensitivity analysis of the model, and refinements to the model.

Grades: 50% for the exams, 30% for the project, 20% for the homeworks.
The 50% for the exams is broken down as 10% for your worst exam and 20% for each of your best two exams. For the purposes of Mid-Term Assessment, exam scores will be posted online, with identifying data removed. Grades will also be posted on LMS.

Textbooks:
The current draft of a new book by Mike Kupferschmid is available on LMS.
These have been used in the past:
J. G. Ecker and M. Kupferschmid; Introduction to Operations Research (Reprinted by Krieger, 2004).
R. L. Rardin; Optimization in Operations Research. Prentice-Hall, 1998.

Textbooks available online:
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. Available on LMS, and online at http://ampl.com/resources/the-ampl-book/
Ferris, Mangasarian, and Wright: Linear Programming with MATLAB. SIAM, 2007. Electronic resource available via the library.
Lee, A First Course in Linear Optimization, Reex Press, 2013–21, available online at https://github.com/jon77lee/JLee_LinearOptimizationBook/blob/master/JLee.4.01.pdf

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

http://www.rpi.edu/~mitchj/matp4700

Office hours:

• in-person: Tuesdays, 2.30-4pm, AE 325. Masks required.

• on webex: Thursdays, 1-3pm, https://rensselaer.webex.com/meet/mitchj

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 Schwendeman.