Operations Research
Bard College

**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, 9th Edition or 10 Edition, by Frederick S. Hillier and Gerald J. Lieberman**Office Hours:**- Monday 4:30 – 5:30pm in RKC 102
- Thursday 3 – 4:30pm in the Learning Commons
- Friday 1 – 5pm in the Learning Commons

**Final:** The Final Exam will be in-class on Monday, May 18. Here are some practice problems for the exam:

- Practice Problems (and Answers)

**Edition 10 (Answers):****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)

**Edition 9 (Answers):****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)

**Edition 7 (Answers):****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)

**Projects:** The final project for this course involves giving a talk on a topic related to Graph Theory.
You can work in groups of 2 or 3 people, or you can work by yourself. The following page contains a list of possible project topics:

**Excel Files:** Here are the Excel files from class:

- From Monday, April 20: Bisection Method and Newton's Method with Excel
- From Wednesday, April 15: Branch and Bound for a BIP with Excel
- From Wednesday, April 8: Solving a Minimum Cost Flow Problem with Excel
- From Monday, March 30: Solving a Transportation Problem with Excel
- From Wednesday, Feb. 4: Solving a Linear Program with Excel.

**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%).

Week |
Dates |
Topics |
Readings |
Homework |

Week 1 | Jan. 26, 28 | Introduction | Chapters 1–3 | |

Week 2 | Feb. 2, 4 | Linear Programming | Chapter 3 | Homework 1 |

Week 3 | Feb. 9, 11 | The Simplex Algorithm | Sections 4.1–4.5 | Homework 2 |

Week 4 | Feb. 16, 18 | More on the Simplex Algorithm | Section 4.6 | Homework 3 |

Week 5 | Feb. 23, 25 | Sensitivity Analysis and Duality | Sections 4.7, 6.1 | Homework 4 |

Week 6 | March 2, 4 | Intro to Game Theory | Sections 14.1–14.3 | Homework 5 |

Week 7 | March 9, 11 | Game Theory | Sections 14.4–14.7 | Homework 6 |

Spring Break | ||||

Week 8 | March 23, 25 | Midterm Exam | ||

Week 9 | March 30, April 1 | The Tranportation and Assignment Problems | Sections 8.1, 8.3–8.5 | Homework 7 |

Week 10 | April 6, 8 | Shortest Path, Minimum Cost Flow | Sections 9.1–9.3, 9.6 | Homework 8 |

Week 11 | April 13, 15 | Integer Programming, Branch and Bound | Sections 11.1–11.7 | Homework 9 |

Week 12 | April 20, 22 | Nonlinear Programming | Sections 12.1–12.6 | Homework 10 |

Week 13 | April 27, 29 | Nonlinear Programming | Sections 12.1–12.6 | Homework 11 |

Week 14 | May 4, 6 | Nonlinear Programming, Presentations | ||

Week 15 | May 11, 13 | Presentations | ||

Week 16 | May 18 | Final Exam |