Download massachusetts institute of technology - James B. Orlin

MASSACHUSETTS INSTITUTE OF TECHNOLOGY
15.058 –Optimization Methods in Operations Research
Spring 2012
Subject Information
15.058 Optimization Methods in Operations Research (New) (
)
Prereq: 18.06 or permission of instructor
Units: 4-0-8
Lecture: TR2.30-4 (E25-111) Recitation: F2.30-4 (E51-149)
Provides an introduction to optimization, building upon the fundamentals of matrix algebra. Covers
optimization methodologies, including linear programming, network optimization, integer programming,
decision trees, and dynamic programming. Applications to logistics, manufacturing, transportation,
marketing, project management, and finance.
Course Staff:
Lecturer:
Recitation instructor:
TAs:
Professor James B. Orlin
Giacomo Nannicini
Zachary Leung
Kurtis McKenney
Subject website:
Grading:
Assignments (2 points each)
In class quizzes (4 points each)
Midterm 1
Midterm 2
Class participation
[email protected]
[email protected]
[email protected]
[email protected]
http://stellar.mit.edu/S/course/15/sp12/15.058/
14%
24%
30%
28%
4%
Problem Sets:
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There are eight 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 another students is not permitted. 1
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.1
Except when stated otherwise, written homeworks should be handed in at the beginning of
class the day on which they are due. For homework sets due on Tuesday, we intend to grade
homework sets and return them at the beginning of class on Thursday. For this reason, late
assignments will not be accepted.
1
Because students are permitted to discuss homework with each other, there may be some legitimate commonalities
in homework solutions, possibly including similar errors. But copying is not permitted. If it appears that students
have “crossed the line,” they will receive a 0 on the homework set. Students receiving a 0 have the opportunity to
appeal.
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Excel spreadsheets should be submitted on line (on the Stellar subject site) by 2:30 PM on the
day in which they are due.
Scores on the eight homework sets will be converted to a grade from 0 to 2 in a nonlinear manner.
That is, if your score on a homework set is P%, then your grade for the homework will be
determined as follows according to what P is.
Any modifications of questions (which may be needed to clarify the question or to correct any
errors) will be emailed to the entire class.
Homework Score


Converted Grade
85% to 100%
2.0
75% to 84.9%
1.5
50% to 74.9%
1.0
25% to 49.9%
0.5
less than 25%
0.0
The lowest homework grade will be dropped.
At the end of the semester, the final homework grade (14% of the course grade) for 15.053 will
be a sum of the converted grades.
Quizzes
 There will be 7 in-class quizzes during the semester, each worth 4% of the final grade. The
lowest quiz score will be dropped.
 The quizzes will be given at the beginning of class and will be 20 to 25 minutes long. It is
especially important for students to arrive on time for those classes.
 The dates of the quizzes are on the syllabus.
 Quizzes will be based on the same material as the problem set due on the day of the quiz.
 There will be no makeup quizzes for unexcused absences; there will be at most one makeup quiz
for an excused absence.
Midterms
 There are two midterms; the second midterm is not “comprehensive.” There is no final exam.
 The subject is not graded on a fixed curve. It’s based on how well students master the material,
as reflected in their subject grade.
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 entirely on the use of clickers throughout the semester.
 Students may not bring another student’s clicker to class.
 While we encourage other forms of participation (such as answering or asking questions in class,
and participation in office hours and recitations), these other forms of participation will not count
for part of the class grade.
Lectures:
 Lectures are given twice weekly.
 In each lecture a new topic is introduced and the theory is presented.
 Lectures include a mixture of presentation of material and interactive exercises.
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No laptops or smart phone usage in class
 Laptops should not be used in class. Exceptions may be made upon request of the instructor.
 Courtesy note: any laptops used in class should be used for note taking only; any other use is not
permitted.
Recitations and Review Sessions.
 Recitation attendance is optional.
 The recitation time is on Fridays from 2:30-4:00 in E51-149. (We may add an additional
recitation if there is sufficient student demand).
 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.
Office Hours.
 The TAs will hold weekly office hours. The times of the office hours will be posted on the
website as soon as they are determined.
 Professor Orlin will hold office hours in his office (E62-570) at a time to be determined.
 Additional help for homework will be available via the web. Hints for problems will be posted
on the subject website.
Textbook and Software
 The textbook for the subject is Applied Mathematical Programming. This book is available on
line at http://web.mit.edu/15.053/www/.
 Microsoft Excel will be used frequently within 15.053. Students will be using the Add-in “Excel
Solver.” Instructions on how to make the add-in available and how to use it are included in the
folder “Excel Information”.
 In addition, Mathematica will also be used a few times during the semester, but it suffices to use
Wolfram CDF Player. You can obtain the CDF Player at this website. You can obtain
Mathematica for free from http://ist.mit.edu/services/software/mathematica/obtain. Mathematica
is also available on Athena.
Subject Content:
15.053 will cover four modules.
Linear Programming Theory and Applications (9 Lectures)
Network Theory and Optimization (5 Lectures)
Integer Programming Theory (4 Lectures)
Decision Trees and Dynamic Programming (3 Lectures)
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Lecture
P.S. Due
dates
1
2
3
PS 1
4
Date
Topic
2/7
Introduction
2/9
Formulations of linear and non-linear programs
2/14
Geometry of linear programs
2/16
5
2/21
The simplex method 1
Quiz 1. LP geometry and the simplex method
The Simplex Method 2
6
2/23
LP in matrix form
2/28
NO CLASS because of President’s Day
Quiz 2. LP in Matrix Form
Duality in linear programming 1
PS 2
PS 3
7
3/1
8
3/6
10
3/13
Duality in linear programming 2
Quiz 3. Duality in LP
Game Theory
Networks 1: Introduction to networks, and the
shortest path problem
11
3/15
Midterm 1.
12
3/20
Networks 2: The maximum flow problem
13
3/22
Networks 3: The minimum cost flow problem
4/3
Networks 4: The network simplex algorithm
4/5
Networks 5. To be determined
4/10
Introduction to integer programming
4/12
Integer programming formulations
4/17
No class today
4/19
IP solution methods 1: Branch and bound
19
4/24
IP solution methods 2: Cutting planes
20
4/26
Decision trees
21
5/1
Midterm 2.
22
5/3
Dynamic Programming 1
23
5/8
5/10
Dynamic Programming 2
Quiz 7. Decision Trees and Dynamic Programming
Lecture topic tbd
5/15
Lecture topic tbd
9
14
PS 4
PS 5
15
16
PS 6
17
18
24
25
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PS 7
PS 8
3/8
26
5/17
Final Class
Dates for Midterms and Review Sessions
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Midterm 1 (covers lectures 1 to 9). In class, on Thursday, March 15.
Review session: Tuesday March 14, 7:00 PM to 8:00 PM.
Midterm 2 (covers lectures 10 to 19). In class, on Tuesday, May 1.
Review session: Monday April 30, 7:00 PM to 8:00 PM.
MIT Sloan Policy on Classroom Behavior
The following policy applies to all subjects at Sloan, as articulated by the Dean of the
Sloan School.
In order to create a productive learning environment and to ensure mutual respect it is essential
that the norms and rules of classroom etiquette and behavior reflect the highest standards. It is
also important that these norms be consistently enforced by the faculty across all classes.
Therefore it is the policy of the MIT Sloan School that

Students are expected to arrive promptly on time and to stay for the entire class. Faculty
are expected to begin and end class on time.

Laptops and e-readers may not be open in the classroom except with explicit permission
of the faculty (e.g., when used to deliver an e-course pack or otherwise used as part of the
instructional program or when required by students because of physical or other
challenges)

Cellphones and PDAs may not be used or permitted to ring in the classroom.
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