Operations Research (IE 1081)

Textbook: Introduction to Operations Research, 11th Ed, Hillier & Lieberman, published by McGraw Hill. 2024 edition.

Prerequisites

1. Knowledge of (a) linear algebra, (b) differential calculus, and (c) basic mathematical concepts such as
   sets, functions, vectors, matrices etc.

2. An interest in mathematical methods.

Course Description

This is an introductory course in operations research (OR). The primary emphasis will be on Linear Programming (LP) and its applications (covering formulation of a number of different types of linear models, the simplex algorithm, duality and sensitivity analysis, and the transportation and assignment problems) as well as basics of Mixed Integer Programming (MIP). Other areas such as network flows, nonlinear and dynamic programming will also be covered, with the amount of emphasis depending on the time available.

The tentative order of topics is as follows:

1. modeling with linear programs and solving with a computer

2. simplex algorithm(s) to solve linear programs

3. duality

4. sensitivity analysis

5. basics of mixed integer programming

6. network models

Objectives

• We will develop modeling and analysis skills in deterministic optimization, focusing primarily on linear programming. At the end of the course, students will be able to

• Identify opportunities for the use of optimization.

• Given a problem to optimize, identify an objective and constraints and model these correctly as a mathematical program. In particular, decide on an appropriate type of model as well as appropriate decision variables. Also, recognize problems that can be more appropriately addressed with approaches other than math programming.

• Use a computer to solve a mathematical program by correctly expressing the problem as valid input for a solver and interpret the results, including sensitivity analysis.

• Communicate intelligently with a coworker or boss about the limits of the model, the solution to the problem, and any corresponding analysis

Applicable ABET Outcomes

1. an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics

2. an ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors

3. an ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions

Assessment

Exams: There will be a midterm and a final exam; the format and dates of the exams will be specified later. If you must miss an exam, you should make alternative arrangements with the instructor before the exam is given. If you miss an exam without prior notification, you will receive a score of zero for that exam, except under very unusual circumstances.

Homeworks: There will be ten homeworks. The lowest three homework grades will be dropped (this applies to groups as well). Homeworks submitted 1–24 hours late will incur a 10% penalty. Homeworks may be completed either in groups of 3–4 or individually. For group homeworks, half of your homework grade will be based on peer review. If you complete the homeworks individually, half of your homework grade will be based on an oral exam. You may opt to complete your homework individually at any point.

Except in extraordinary circumstances any homework that is turned in later will get zero points and there will be no make up homeworks. 

Group homeworks: 

• The instructor will assign groups based on the results of a survey. Homework groups must meet at least once before each homework is due. Students should come to these meetings having attempted all of the homework questions. The group should then work together to carefully prepare a single submission. 

• At the end of the semester, group members will rate one another on the following aspects: (i) respectfulness, (ii) preparedness for meetings, (iii) contribution to group discussions of the homework, (iv) communication and (v) helpfulness.

• Students may choose at any time to switch to the oral-exam option, including if they are dissatisfied with the outcome of the peer-review assessment. Homework oral exams will take place during the final week of classes.

Homework oral exam (optional): Students will be given a randomly selected homework that they or their group submitted and will be asked related questions about it by the TA.

Grading: Midterm Exam 25%, Final Exam 40%, Homework 15%, in class group exercises 5% + 2% bonus, two quizzes 15%

If you miss a quiz or in class group exercise you need promptly schedule an appointment with the TA to make up. 

LLM usage: Do not use AI to generate answers to homeworks. Copying AI output is prohibited. More importantly, relying on AI harms your learning and will not prepare you well for exams, where AI is not allowed. It is important to be aware that AI, which has read almost every textbook in existence (and the answers to all the exercises) does much better at homework problems than real world problems which are much more messy, complicated and ambiguous (but unfortunately beyond the scope of this introductory course). If there is suspicion of AI usage, or team members failing to contribute to a group the instructor reserves the right to replace the whole of the students homework grade with a homework oral exam.

Regrades: The TA grades all homework assignments, so please direct any questions about homework grades to the TA before contacting the instructor. If you have a question about your midterm grade, please come to office hours. To request a regrade of the midterm, you must submit the Midterm Regrade Request Form available on Canvas. The entire midterm will be regraded, and your score may increase or decrease.

Standard University Policies

Academic Integrity

All students are expected to adhere to the standards of professional conduct and academic honesty. Any student engaged in cheating, plagiarism, or other acts of academic dishonesty would be subject to disciplinary action. Any student suspected of violating this obligation for any reason during the semester will be required to participate in the procedural process, initiated at the instructor level, as outlined in the SSOE Academic Integrity Policy found at: https://www.engineering.pitt.edu/Academic-Integrity-Guidelines/.

Disability Services

If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services (DRS), 140 William Pitt Union, (412) 648-7890, drsrecep@pitt.edu, (412) 228-5347 for P3 ASL users, as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.

Statement on Classroom Recording

To ensure the free and open discussion of ideas, students may not record classroom lectures, discussion and/or activities without the advance written permission of the instructor, and any such recording properly approved in advance can be used solely for the student’s own private use. Class will not be recorded. If students are absent they should talk with the professor on how to make up for their absence. For example, attend office hours.

Student Opinion of Teaching Surveys

Students in this class will be asked to complete a Student Opinion of Teaching Survey. Surveys will be sent via Pitt email and appear on your Canvas page during the last three weeks of class meeting days. Your responses are anonymous. Please take time to thoughtfully respond, your feedback is important to me.

Diversity and Inclusion

The University of Pittsburgh does not tolerate any form of discrimination, harassment, or retaliation based on disability, race, color, religion, national origin, ancestry, genetic information, marital status, familial status, sex, age, sexual orientation, veteran status or gender identity or other factors as stated in the University’s Title IX policy. The University is committed to taking prompt action to end a hostile environment that interferes with the University’s mission. For more information about policies, procedures, and practices, see: http://diversity.pitt.edu/affirmative-action/policies-procedures-and-practices.

I ask that everyone in the class strive to help ensure that other members of this class can learn in a supportive and respectful environment. If there are instances of the aforementioned issues, please contact the Title IX Coordinator, by calling 412-648-7860, or e-mailing titleixcoordinator@pitt.edu. Reports can also be filed online:
https://www.diversity.pitt.edu/make-report/report-form. You may also choose to report this to a faculty/staff member; they are required to communicate this to the University’s Office of Diversity and Inclusion. If you wish to maintain complete confidentiality, you may also contact the University Counseling Center (412-648-7930).

Acknowledgements

The course material was based on material developed by Dr. Prokopyev.