Syllabus
 Introduction (PDF)
 Formulations of linear and nonlinear programs (PDF)
 Geometry and visualizations of linear programs (PDF)
 The simplex method 1 (PDF)
 The simplex method 2 (PDF)
 Sensitivity analysis and shadow prices (PDF)
 Game theory 1: 2person 0sum, or constant sum (PDF)
 Game theory 2 (PDF)
 Discussion of projects; slack variables vs. artificial variables (PDF)
 Introduction to integer programming (PDF)
 Integer programming formulations (PDF)
 Integer programming techniques 1: branch and bound (PDF)
 Integer programming techniques 2: cutting planes (PDF)
 Integer programming formulations, again (PDF)
 Networks 1: Shortest path problem (PDF)
 Networks 2: Network flows (PDF  1.4MB)
 Networks 3: Traveling salesman problem (PDF)
 Decision trees 1 (PDF)
 Decision trees 2: the value of information (PDF)
 Behavioral economics (PDF)
 Recitation 1 problems (PDF)
 Recitation 1 solutions (PDF)
 Recitation 2 problems (PDF)
 Recitation 2 solutions (PDF)
 Recitation 3 problems (PDF)
 Recitation 3 solutions (PDF)
 Recitation 4 problems (PDF)
 Recitation 4 solutions (PDF)
 Recitation 5 problems (PDF)
 Recitation 5 solutions (PDF)
 Recitation 6 problems (PDF)
 Recitation 6 solutions (PDF)
 Recitation 7 problems (PDF)
 Recitation 7 solutions (PDF)
 Recitation 8 problems
 Recitation 8 solutions (PDF)
 Recitation 9 problems (PDF)
 Recitation 9 solutions (PDF)
 Recitation 10 problems (PDF)
 Recitation 10 solutions (PDF)
 Problem Set 1 – Group 1 (PDF)
 Problem Set 1 solutions – Group 1 (PDF)
 Problem Set 2 – Group 1 (PDF)
 Problem Set 2 solutions – Group 1 (PDF)
 Problem Set 3 (PDF)
 Problem Set 4 (PDF)
 Problem Set 4 solutions (PDF)
 Problem Set 5 (PDF)
 Problem Set 5 solutions (PDF)
 Problem Set 6 (PDF)
 Problem Set 6 solutions (PDF)
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. AddisonWesley, 1977. ISBN: 9780201004649.
Microsoft^{®} Excel will be used frequently within 15.053. Students will be using the "Solver" Addin 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 spreadsheetbased) 
10% 
Spreadsheets 
10% 
Inclass 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 nonlinear 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: 2person 0sum, 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 inclass 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 