Optimization Methods in Management Science


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1.5 hours / session


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.

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.


Problem sets

Written (not spreadsheet-based)




In-class quizzes

Quiz 1 (practice)


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.


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.


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.



L = Lecture session

R = Recitation session

L1 Introduction  
L2 Formulations of linear and non-linear programs  
R1 Recitation 1  

Geometry and visualizations of linear programs

Quiz 1: Formulations

Problem set 1 due
L4 The simplex method 1  
R2 Recitation 2  

The simplex method 2

Quiz 2: Formulations and LP geometry

Problem set 2 due
R3 Recitation 3  
L6 Sensitivity analysis and shadow prices  

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  

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  

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  

Decision trees 1

Quiz 6: Networks

L19 Decision trees 2: the value of information  
R10 Recitation 10  

Behavioral economics 1

Quiz 7: Decision trees

Project: final team paper and individual learning due
L21 Behavioral economics 2  
L22 Project reports  

Project reports

Final feedback