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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: 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. Page 1 of 5 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. Page 2 of 5 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) Page 3 of 5 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 Page 4 of 5 PS 7 PS 8 3/8 26 5/17 Final Class Dates for Midterms and Review Sessions 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. Page 5 of 5