MATH 430 D Operations Research

Dr. Fenton Fall 2007

Mondays, Wednesdays, and Fridays, 11:00-11:50 in Pasteur 106

Web page: http://www.bellarmine.edu/faculty/fenton/

A. INTRODUCTION

This course is an introduction to topics and algorithms in Operations Research, in particular the deterministic aspects of the field. (Deterministic means that it is possible to find definite answers to the problems, that is, probability is not involved. However, there will be a few times when we use a little probability.) Operations Research was developed in the mid 20th century to address problems of logistics and planning, originally for military needs but also for managing large corporations. It is therefore the most modern mathematics taught at Bellarmine University.

The topics include: linear programming, the simplex method, duality, sensitivity analysis, important variations of linear programming, integer programming, network analysis, and game theory. Specifically, we will cover Chapters 1 - 6, parts of Chapter 8 and Chapter 9, plus Chapters 11, 14, and 22, though not in that order. We will use the software that comes with the textbook.

In this course, you will work in groups for the homework, for work in class, and for portions of the two tests. You must choose your group no later than Monday September 4.

While I will attempt to follow this syllabus in every detail, circumstances may require changes to the course as the semester progresses.

B. CONTACTING THE INSTRUCTOR

My office is Pasteur Hall 006-F, phone 452-8430. My office hours are 12:00-12:50 Mondays, Tuesdays, Wednesdays, and Fridays. I am in my office a great deal when I am not in class; please feel free to stop by. Messages may be left in my mailbox in Pasteur 006. You can contact me electronically either on the campus network or at wfenton@bellarmine.edu. Feel free to phone me at home at 454-7855 (but not after 9:00 p.m. please).

C. COURSE DESCRIPTION (from the University Catalog)

"An introduction to deterministic optimization. Topics include linear programming, sensitivity analysis, duality theory, network analysis, integer programming, and game theory."

D. PREREQUISITE

This course has Math 215 as its prerequisite. Certain concepts from Linear Algebra are crucial for understanding the theory of the simplex method. Also, we will work a great deal with matrices. Although we will use the computer, we will not do any programming.

E. REQUIRED TEXT

Introduction to Operations Research, 8th edition by Hillier & Lieberman

F. GOALS & OBJECTIVES

By the end of the semester, a successful student should be able to

interpret certain types of problem situations mathematically and construct mathematical models to describe them;
chose an appropriate algorithm to solve each of these mathematical models;
carry out each algorithm and explain generally why it works; and
interpret the results of the calculations in the original problem setting.

Learning Objectives	How proficiency will be demonstrated
General Education Goal 8: Quantitative reasoning using graphical and symbolic representations	This will be demonstrated in class discussions, on homework, and on exams.
Department Goal 1: Students should develop skills in problem-solving.	This will be demonstrated on homework and on exams.
Department Goal 2: Students should develop their ability to communicate mathematical ideas.	Class discussions will require informal oral communication. Homework and exams will require more formal written communication.
Department Goal 4: Students should be aware of a broad variety of applications, both in and out of mathematics.	The course includes an introduction to optimization in applied settings. This will be demonstrated on homework and on exams.
Department Goal 5: Students should recognize the breadth of mathematics and experience the intellectual rigor of depth in an advanced subject area.	This course builds on students’ backgrounds in linear algebra and discrete mathematics, and thus provides depth in a mathematical subject. This will be demonstrated on homework and on exams.

G. ATTENDANCE

This is entirely up to you. However, you are responsible for all material discussed in class. In my experience, people who come to class regularly usually have a better understanding of the material than those who miss classes.

H. GRADING

There are several components to your grade, as shown below. You must take all the exams and submit a paper to pass the course.

Homework 8 assignments at 25 points each = 200 points

Test 1 Ch. 1, 2, 3, 4, 5 150 points

Test 2 Ch. 6, 8, 11 150 points

Paper 100 points

Final Exam Wednesday April 28, 8:00 all material 250 points

TOTAL 850 points

Homework is to be done with your group. Everyone who works on an assignment should sign the first page, certifying that he/she participated fully in the work. The homework will be collected and graded, 25 points per assignment. These assignments are listed on a separate page. The test questions will be similar to the homework problems.
Each test will be in two sections, a group portion to be done as a take-home exam and an individual portion to be done in class. Make-up tests will be given only in extreme circumstances and only if I am contacted on or before the day of the test.
TEST 1: This will be in two portions, a 50 point group portion and a 100 point individual portion. This is tentatively scheduled for Friday October 12; we will set specific dates as we finish Chapter 5.
TEST 2: This also will be in two portions, a 50 point group portion and a 100 point individual portion. This is tentatively scheduled for Friday November 16; we will set specific dates as we finish Chapter 11.
The paper will examine an application of Operations Research. This is discussed in more detail below.
The Final Exam will be MONDAY DECEMBER 10 at 11:30-2:30. It will be comprehensive, covering the entire semester but with extra emphasis on the material since the second test. It is solely an individual test.

Grades will be assigned on the following scale.

A [92, 100%] B+ [84,88) C+ [70, 75) D [50, 60)

A- [88, 92) B [79, 84) C [60, 70) F [0, 50)

B- [75, 79)

The course grade will be your point total as a percentage of the 850 possible points.

I. UNIVERSITY POLICIES

Academic Honesty

I strongly endorse and will follow the academic honesty policy as published in Bellarmine’s Catalog 2007-2009 (pp. 48-49) and in the Student Handbook; both documents are available online via the student portal on the University’s intranet. Students must be fully aware of what constitutes academic dishonesty; claims of ignorance cannot be used to justify or rationalize dishonest acts. Academic dishonesty can take a number of forms, including but not limited to cheating, plagiarism, fabrication, aiding and abetting, multiple submissions, obtaining unfair advantage, and unauthorized access to academic or administrative systems or information. Definitions of each of these forms of academic dishonesty are provided in the academic honesty section of the Student Handbook. All detected instances of academic dishonesty will be reported to the Provost, and sanctions will be imposed as dictated by the policy. Penalties range from failing an assignment or test to dismissal from the University, depending, in part, on the student’s previous record of academic dishonesty. On the second offense during a student’s academic career, as a minimum additional penalty, the Provost will immediately suspend the student for the semester in which the most recent offense took place. On the third offense, the Provost will immediately dismiss the student from the University.

Disability Policy (from the Student Handbook)

“Students with disabilities who require accommodations (academic adjustments and/or auxiliary aids or services) for this course must contact the Disability Services Coordinator (Room 225 Horrigan Hall or 452-8150). Please do not request accommodations directly from the professor.”

Travel Policy

The University requires students who will be absent from class while representing the University to inform their instructors in two steps. During the first week of the course, students must meet with each instructor to discuss the attendance policy and arrangements for absences related to University-sponsored events. Second, students must provide the instructor with a signed Student Absentee Notification Form, available via the student portal on the University intranet, at the earliest possible opportunity, but not later than the week prior to the anticipated absence. The Student Absentee Notification Form does not serve as an excused absence from class. Your instructor has the final say about excused and unexcused absences and it is the student’s responsibility to know and abide by the instructor’s policy.

HOMEWORK ASSIGNMENTS

Assignment	Chapter	Tentative due date	Pages	Problems
#1	3	Wednesday Sept. 5	91-96	3.1 - 1, 4, 8, 10, 11 3.2 - 2, 3, 4, 5 3.3 - 1, 2 3.4 - 1, 3, 7, 10
#2	4	Monday Sept. 24	162-169	4.1 - 1, 4, 8 4.2 – 1ab 4.3 - 1, 7 4.4 - 1, 7 4.5 - 1, 4, 8 4.6 - 1, 3, 8, 11, 13, 14, 17 4.7 – 5
#3	5	Friday Oct. 5	202-207	5.1 – 1, 4, 10, 14, 16, 17, 18, 20, 21 5.3 - 1, 2, 5
Test 1
#4	6	Friday Oct. 19	276-283	6.1 - 1, 2, 3, 8, 11 6.3 - 1, 4, 5 6.4 – 1, 3, 4 6.5 – 1 6.6 – 2 6.7 - 1, 7
#5	8	Wednesday Oct. 31	364-371	8.1 - 1, 2, 3 8.2 – 1c, 5, 6, 8, 11, 21abcd 8.3 – 1ab, 2, 4 8.4 - 1, 4, 6
#6	11	Friday Nov. 9	534-542	11.1 – 2ac, 4, 5 11.3 – 1, 4, 5, 7 11.4 – 1, 5 11.5 - 1, 5 11.6 - 1, 2, 6 11.7 – 1, 5, 8, 9
Test 2
#7	9	Friday Nov. 30	428-431	9.2 – 1 9.3 - 2, 3, 6 9.4 - 1, 2, 3 9.5 - 1, 3ab, 4abcd
	22		22:42-47 on the disk	22.2 – 1, 2 22.3 – 2, 3 22.4 – 1, 2
#8	14	Friday Dec. 7	675-678	14.1 - 1, 3 14.2 - 1, 2, 3, 4, 5, 6 14.4 – 2, 3 14.5 - 1, 2
Final Exam		Monday Dec. 10

THE PAPER

Since Operations Research began as a very applied area of mathematics, and continues to be so, I want you to see a more specific application than the topics discussed in class. You are required to write a summary of one of the articles in the attached list. Identify the method or methods used in the article (linear programming, integer programming, transportation problem, etc.). Explain how the algorithm(s) were used in the article and applied to the particular situation. I am particularly interested in the underlying mathematics used in the application.

Your paper will be graded by the following rubric:

Outstanding (100 pts.)	The paper has a clear introduction previewing the topic. The main points are clearly stated and well organized. There is a clear conclusion summarizing the topic. The mathematics is correct. Diagrams are clear and accurate, and integrated into the report. The level of presentation is appropriate for the audience. Sources are properly cited and a correct bibliography is included. The paper uses correct grammar and spelling (no slang!). Two copies are submitted, and a copy of the article.
Good (80 pts.)	The paper has an introduction and a conclusion. The paper lacks some organization. Some main points are not clear. The mathematics has only minor errors. The level of presentation is almost always appropriate for the audience. Diagrams lack some clarity or are not integrated into the paper. Sources are given and a bibliography is included. The paper has only minor difficulties with grammar or spelling. Two copies are submitted, and a copy of the article.
Minimal (60 pts.)	The paper lacks an introduction or conclusion. The paper is poorly organized. Main points are not clear. The mathematics has significant errors. Diagrams are needed but not included. The level of presentation does not match the audience. No sources are given or the bibliography is missing. The paper has significant difficulties with grammar or spelling. Only one copy is submitted, or a copy of the article is not submitted.
Not acceptable (0 pts.)	No report is submitted.

Some specific requirements:

Your selection, including a copy of the article, must be turned in no later than Friday, Sept. 28. Everyone must write on a different article, so the first person to turn in a selection gets that article. I will deduct 5 points for each day this is late.
Four to six pages, not including any diagrams
Double-spaced in 12-pt. font, with page numbers
Turn in two copies of the paper and a copy of the article.
The paper is due on Wednesday, November 28 at the beginning of class; later that day is LATE!
I will deduct 10 points for each day the paper is late.