Operations Research Bard College

## Operations Research

• Professor: Maria Belk
• Office: The Learning Commons, Stone Row basement
• Email: mbelk@bard.edu
• Class schedule: Monday 3:10–4:30pm in RKC 102
• Textbook: Introduction to Operations Research, 10 Edition, by Frederick S. Hillier and Gerald J. Lieberman
• Office Hours:
• Wednesday 1–3pm
• Friday 2–5pm

## Announcements

Final Exam: The Final Exam will be in-class on Monday, May 21. Here are some practice problems for the exam:

And here are some practice problems from the textbook along with answers to the non-starred problems (starred problems from the textbook have answers in the back of the book).
• Chapter 9: 9.1–3(b), 9.3–4(a)
• Chapter 10: 10.3–2(a)(b), 10.3–4, 10.6–3
• Chapter 12: 12.1–2(a), 12.3–1(a), 12.3–7(a), 12.7–2(b)
• Chapter 13: 13.5–1(a)(b), 13.6–8 (a)
• Chapter 8: 8.1–3(b), 8.3–4(a)
• Chapter 9: 9.3–2(a)(b), 9.3–4, 9.6–3
• Chapter 11: 11.1–2(a), 11.3–1(a), 11.3–7(a), 11.7–2(b)
• Chapter 12: 12.5–1(a)(b), 12.6–8 (a)
• Chapter 8: 8.1–2(b), 8.3–4(a)
• Chapter 9: 9.3–1(a)(b), 9.3–3, 9.6–2
• Chapter 12: 12.1–2(a), 12.3–1(a), 12.3–7(a), 12.7–1(b)
• Chapter 13: 13.5–1(a)(b), 13.6–10 (a)

Project: The final project for this course involves giving a talk on a topic related to Operations Research. You can work in groups of 2 or 3 people, or you can work by yourself. See the following link for information on the project, including possible topics:

Excel: Here are some of the Excel Spreadsheets from class:

• BisectionAndNewtonsMethod.xlsx: This is the Excel spreadsheet that used the Bisection Method and Newton's Method to find a local maximim. The Bisection Method is used on the first sheet, and Newton's Method is on the second sheet.
• BranchAndBoundBIP.xlsx: This is the Excel spreadsheet that used Branch and Bound to solve a binary integer program.
• MinimumCostFlow.xlsx: This is the Excel spreadsheet that solved the Minimum Clost Flow Problem from class on April 9.
• OperationsResearchJan31.xlsx: This is the Excel spreadsheet from class on January 31.

## Course Requirements

• Homework: There will be weekly homework assignments. I encourage you to work with others on the homework assignments; mathematics is generally easier and more enjoyable when working with others. You should write up your own solutions independently and acknowledge all collaborators.
• Exams: There will be two in-class exams: a midterm and a final.
• Project: There will be one project consisting of a class presentation. You can work on the project indivdually or in groups of two or three. More details about the project will be given later in the semester.

Your grade will be based on homework assignments (40%), two in-class exams (40%), and a project (20%).

## Assignments and Tentative Syllabus

 Week Dates Topics Readings Homework Week 1 Jan. 29, 31 Introduction Chapters 1–3 Homework 1 Week 2 Feb. 5, 7 Linear Programming Chapter 3 Homework 2 Week 3 Feb. 12, 14 The Simplex Algorithm Sections 4.1–4.5 Homework 3 Week 4 Feb. 19, 21 More on the Simplex Algorithm Section 4.6 Homework 4 Week 5 Feb. 26, 28 Sensitivity Analysis and Duality Sections 4.7, 6.1 Homework 5 Week 6 March 5, 7 Intro to Game Theory Sections 14.1–14.3 Homework 6 Week 7 March 12, 14 Game Theory Sections 14.4–14.7 Spring Break Week 8 March 26, 28 Midterm Exam Homework 7 Week 9 April 2, 4 The Tranportation and Assignment Problems Sections 8.1, 8.3–8.5 Homework 8 Week 10 April 9, 11 Shortest Path, Minimum Cost Flow Sections 9.1–9.3, 9.6 Homework 9 Week 11 April 16, 18 Integer Programming, Branch and Bound Sections 11.1–11.7 Homework 10 Week 12 April 23, 25 Nonlinear Programming Sections 12.1–12.6 Homework 11 Week 13 April 30, May 2 Nonlinear Programming Sections 12.1–12.6 Week 14 May 7, 9 Nonlinear Programming, Presentations Week 15 May 14, 16 Presentations Week 16 May 21 Final Exam