MATH 381-01 [7067], Fall 2016
Linear Methods of Operations Research

Course information

Course: MATH 381-01 [7067]: Linear Methods of Operations Research

Time/Place: TuTh 11:30pm-12:45pm, SOND 108

Instructor: Dr. Jacob Kogan Grader: Tessa Helble

Office: MP 426

Phone: 410-455-3297

Email: kogan at math.umbc.edu tess2@umbc.edu

Office hours: TuTh 1:30 PM-2:30 PM and by appointment

Textbook

An Introduction to Linear Programming and Game Theory (third edition) by Thie and Keogh, Wesley, 2008.

Course Contents

Chapter 1, Sections 1.1-1.4
Chapter 2, Sections 2.1-2.6
Chapter 3, Sections 3.1-3.9
Chapter 4, Sections 4.1-4.5
Chapter 5, Sections 5.1-5.7
Chapter 6, Sections 6.1-6.4
Chapter 7, Sections 7.1-7.3
Chapter 9, Sections 9.1-9.7

We may cover these topics in a different order. Depending on time we may cover more (or delete) topics.

Supplementary Course Materials

LP Assistant & LINDO: These are very user-friendly computer software that we will use to numerically solve linear programs and related problems. You can obtain LP Assistant from one of the authors, Jerry Keough's website. The student version of LINDO (Classic LINDO) can be obtained from LINDO website. I recommend that you get familiar with both software packages as soon as possible, and try LINDO as early as Chapter 2, on homework.

Course Description/Learning Objectives

This is an introductory course in Linear Programming, covering its applications, and computational aspects. Linear Programming is an important subject with wide range of industrial applications.

We will first learn how to formulate real-life problems as linear programs.
We will then learn how to solve an already formulated linear program using the simplex method, both by hand and using the LP Assistant and LINDO software mentioned above.
After that, we learn about the important duality concept in linear programming, and use it to study sensitivity analysis of a linear program.
Finally, several special classes of linear programs warrant special attention. We consider several of these towards the end of the course.

The official mathematical prerequisite for this course is Linear Algebra, which is relatively modest for a mathematics course at this level (high 300s). However, you will use computational linear algebra tools such as pivoting extensively, and you will need to be able to carry out these computational steps efficiently, and correctly. In addition more theoretical linear algebra will be needed in the form of matrix algebra, in order to understand the concepts of duality and sensitivity analysis. Moreover, already at the beginning of the course and throughout, you will need a good deal of mathematical maturity for modeling linear programs.

Policy on Homework and Exams

Your success in this course depends greatly on you doing the assigned homework assignments regularly to assimilate the material covered in the classes.
The homework problems will be listed on the course web page. Please make sure that you finish the homework on time and that you bring the difficulties to my attention.
Wholesale answers to homework problems will not be given. If you are unsure whether your solution to a particular problem is correct, you take advantage of the office hours.
There will be no make up tests.
Calculators are not allowed in examinations.

General Advice on How to Study for the Course

The instructor is available to guide you and to give you directions. However, you are ultimately responsible for your own learning.
To be successful in the course, you should devote 10-15 hours per week studying for it (more if you need to). It is imperative that you keep up with the material. It is equally imperative to have good study habits. When studying for this course, you should always have pen and pencil ready. If you are studying without them, you are probably wasting your scarce time.
It is very important that you come to each class having read the material to be covered that day. (You will need to read this material several times anyway!) Reading it in advance will help you to understand the lecture better. It also gives you a chance to ask questions about the parts you did not understand fully.
Studying in groups may be a good idea for some things. However, you should not rely on group study alone. Best learning is done alone, and by leaving plenty of time for self-reflection.
You should come and ask questions during the office hours. This is the time I am available exclusively to answer your questions; make good use of it.

Homework, Quizzes, Tests, and Grading

Homework : Weekly homework will be assigned on Thursday and discussed the following Tuesday.
Grading : The final grade will be based on three midterms (33 pt each), and the comprehensive final (100 pt).

Date	Points	Topic	Test	Solutions
Test 1, Thursday, September 8	33 pt	topics to be covered	test 1	test 1
Test 2, Thursday, October 20	33 pt	Sec. 2.2-2.5, 3.1-3.9, 4.1-4.4	test 2	test 2
Test 3, Thursday, December 1	33 pt	Sec. 4.5, 5.1-5.7	test 3	test 3
Final, Thursday, December 15	100 pt	material covered over the semester

The final exam is on Thursday, December 15 from 10:30 am to 12:30 pm. There will be no make up tests. Letter grade cutoffs are expected to be the following:

Percentage	≥ 90%	89% ≥ and ≥ 80%	79% ≥ and ≥ 70%	69% ≥ and ≥ 60%	59% ≥
Letter Grade	A	B	C	D	F

The grading system may be changed for the entire class or in individual cases at the discretion of the instructor. In particular, class attendance and participation, steadily improving grades on exams and quizzes, may earn you the better grade if your score falls on the borderline between two grades.

Remember: Mathematics is NOT a spectator sport.
Read through the relevant section of the text (and look over all the assigned problems) before each lecture.

Homework assignments

solutions

Sec. 2.2, p. 17: 6, 10a, 10b, 10c, 10d
Sec. 2.3, p. 26: 1, 9, 11
HW1 due Tuesday 09/13/16 ends here
HW2 due Tuesday 09/20/16 starts here solutions and solutions
Sec. 2.4, p. 36: 2, 6
Sec. 2.5, p. 43: 3, 7, 10
Sec. 3.1, p. 60: 2, 3, 7
Sec. 3.2, p. 70: 3, 4, 6, 9
HW2 due Tuesday 09/20/16 ends here
HW3 due Tuesday 09/27/16 starts here solutions
Sec. 3.3, p. 76: 1, 2, 4
Sec. 3.4, p. 83: 2, 4, 7, 9
HW3 due Tuesday 09/27/16 ends here
HW4 due Tuesday 10/04/16 starts here solutions
Sec. 3.5, p. 89: 2(a,b,c), 3, 6(a), 7
HW4 due Tuesday 10/04/16 ends here
HW5 due Tuesday 10/11/16 starts here solutions
Sec. 3.6, p. 98: 1, 2(b, f), 8
Sec. 3.9, p. 113: 8, 11, 13, 14
HW5 due Tuesday 10/11/16 ends here
HW6 due Tuesday 10/18/16 starts here solutions
Sec. 4.2, p. 130: 1, 3
Sec. 4.3, p. 136: 4a, 5ab
Sec. 4.4, p. 149: 2, 3, 6, 10ab
HW6 due Tuesday 10/18/16 ends here
no homework due October 25, 2016-take a look at test 2 solution.
HW7 due Tuesday 11/01/16 starts here solutions
Sec. 4.5, p. 159: 1, 2, 3(a,b,c,d)
HW7 due Tuesday 11/01/16 ends here
HW8 due Tuesday 11/08/16 starts here solutions
Sec. 5.1, p. 169: 7, 13, 17
Sec. 5.2, p. 181: 1, 3, 7
HW8 due Tuesday 11/08/16 ends here
HW9 due Tuesday 11/15/16 starts here solutions
Sec. 5.3, p. 187: 3, 7, 12
Sec. 5.4, p. 191: 1, 3, 6
HW9 due Tuesday 11/15/16 ends here
HW10 due Tuesday 11/22/16 starts here solutions
Sec. 5.5, p. 195: 1, 4, 8
Sec. 5.6, p. 203: 3, 5
Sec. 5.7, p. 208: 2, 4
HW10 due Tuesday 11/22/16 ends here

The Official UMBC Honors Code

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal.

To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, the UMBC Integrity webpage www.umbc.edu/integrity, or the Graduate School website http://www.umbc.edu/gradschool/procedures/integrity.html.

Course:	MATH 381-01 [7067]: Linear Methods of Operations Research
Time/Place:	TuTh 11:30pm-12:45pm, SOND 108
Instructor:	Dr. Jacob Kogan	Grader:	Tessa Helble
Office:	MP 426
Phone:	410-455-3297
Email:	kogan at math.umbc.edu		tess2@umbc.edu
Office hours:	TuTh 1:30 PM-2:30 PM and by appointment

MATH 381-01 [7067], Fall 2016 Linear Methods of Operations Research