## Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1.5 hours / session

## Prerequisites

This subject has no formal prerequisites.

## Course Structure

15.053 is structured as two longer modules followed by three short modules.

- Linear Programming Theory and Applications (7 Lectures)
- Integer Programming Theory (5 Lectures)
- Network Flows and Heuristics (3 Lectures)
- Decision Trees (2 Lectures)
- Behavioral Economics (2 lectures)

See the calendar below for more details.

## Textbook and Software

There is no required textbook for the subject. Students can refer to the following book, out of print but available free online, for some of the material.

- Bradley, S. P., A. C. Hax, and T. L. Magnanti.
*Applied Mathematical Programming*. Addison-Wesley, 1977. ISBN: 9780201004649.

Microsoft^{®} Excel will be used frequently within 15.053. Students will be using the "Solver" Add-in that is available when Microsoft^{®} Office or Excel is installed.

The class will use Piazza for online discussions and announcements.

## Grading

COURSE WORKS | PERCENTAGES |
---|---|

Problem sets | |

Written (not spreadsheet-based) | 10% |

Spreadsheets | 10% |

In-class quizzes | |

Quiz 1 (practice) | 0% |

Quizzes 2 to 5 | 10% (2.5% each) |

Quizzes 6 and 7 | 10% (5% each) |

Midterm 1 | 20% |

Midterm 2 | 20% |

Team Project | 15% |

Class Participation | 5% |

## Problem Sets

There are six problem sets. Problem sets are an important part of the learning experience, which is why they are required.

Problem sets are to be handed in individually; however, students may discuss the problems with others in the class. Copying from other students is not permitted.

Spreadsheets should also be individual work. Students may obtain help from other students. But students may not copy and paste parts of spreadsheets from other students.

## Quizzes

There are seven quizzes. Quizzes are given at the beginning of class periods as noted on the calendar, and will be 20 to 30 minutes long. Quizzes will be based on the same material as the problem set due on the day of the quiz.

- The first quiz is for practice, but it may count as part of the quiz grade if its inclusion leads to an increase in the average quiz score.
- The lowest score in quizzes 2 to 5 will be dropped. The scores of the remaining quizzes will be scaled so that the grade is out of 10 points.
- The topics of Quizzes 2 to 5 appear again on the two midterms.
- Quizzes 6 and 7 are both required. They cover the topics that are presented after the second midterm.
- Quizzes 6 and 7 are worth 5 points each. They are worth more than other quizzes because the material is not tested again.

## Exams

There are two midterms. The first is on linear programming; the second is on integer programming. The second midterm is not "comprehensive," but integer programming concepts do build on linear programming.

There is no final exam.

## Team Project

15.053 aims to teach students methods for identifying and solving optimization problems. In order to bring these concepts to life, students will be preparing group projects to identify and model a real world optimization problem. The student teams will select an actual situation and use the concepts from class to define the problem, build an optimization model, and solve it.

Final project deliverables include a 4 to 6 page team paper, a 1 page written assessment of individual learnings, and a team presentation.

## Class Participation

Students will be provided clickers at the second lecture of the semester, which the student can keep for the entire semester. Students should bring their clickers to each class.

Class participation points will be based on the use of clickers throughout the semester.

Students may not bring another student's clicker to class.

## No Laptops or Smart Phone Usage in Class

Laptops should not be used in class, except by students who have been granted an exception to use them for notetaking only. Any other use is not permitted.

## Recitations and Review Sessions

Recitation attendance is optional. Recitations will cover problems that are similar to the ones on the current problem set.

In addition, there will be a review session the night before each of the two midterms.

## Calendar

Key:

L = Lecture session

R = Recitation session

SES # | TOPICS | KEY DATES |
---|---|---|

L1 | Introduction | |

L2 | Formulations of linear and non-linear programs | |

R1 | Recitation 1 | |

L3 |
Geometry and visualizations of linear programs Quiz 1: Formulations | Problem set 1 due |

L4 | The simplex method 1 | |

R2 | Recitation 2 | |

L5 |
The simplex method 2 Quiz 2: Formulations and LP geometry | Problem set 2 due |

R3 | Recitation 3 | |

L6 | Sensitivity analysis and shadow prices | |

L7 |
Game theory 1: 2-person 0-sum, or constant sum Quiz 3: The simplex method | Problem set 3 due |

R4 | Recitation 4 | |

L8 | Game theory 2 | |

L9 |
Discussion of projects; slack variables vs. artificial variables Quiz 4: Sensitivity analysis | Problem set 4 due |

R5 | Recitation 5 | |

Midterm exam 1 | ||

L10 | Introduction to integer programming | Project: list of team members due one day prior |

L11 | Integer programming formulations | Project: topic and short description due 2 days later |

R6 | Recitation 6 | |

L12 | Integer programming techniques 1: branch and bound | |

L13 |
Integer programming techniques 2: cutting planes Quiz 5: Integer programming formulations |
Problem set 5 due Project: draft proposal due |

R7 | Recitation 7 | |

L14 | Integer programming formulations, again | |

L15 | Networks 1: Shortest path problem | Problem set 6 due |

R8 | Recitation 8 | |

Midterm exam 2 | Project: final proposal due | |

L16 | Networks 2: Network flows | |

L17 | Networks 3: Traveling salesman problem | Project: class vote on in-class presentations |

R9 | Recitation 9 | |

L18 |
Decision trees 1 Quiz 6: Networks | |

L19 | Decision trees 2: the value of information | |

R10 | Recitation 10 | |

L20 |
Behavioral economics 1 Quiz 7: Decision trees | Project: final team paper and individual learning due |

L21 | Behavioral economics 2 | |

L22 | Project reports | |

L23 |
Project reports Final feedback |