MATH 430
Operations Research
Fall 2013
Dr. Fenton
Web page at http://www.bellarmine.edu/faculty/fenton/
Section 01 meets Tuesdays and Thursdays, 3:05-4:20.
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
software that can be downloaded from the publisher’s website.
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 Tuesday
September 3. For this course, groups may have two or three members.
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 Alumni Hall 202, phone 272-8059. My office hours are 2:00-3:00 Tuesdays
and Thursdays. Messages may be left in my mailbox in Alumni Hall. 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, 9th edition by Hillier & Lieberman, McGraw-Hill.
ISBN 978-0-07-337629-5
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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:
This will be demonstrated in class
Quantitative reasoning using graphical and discussions, on homework, and on exams.
symbolic representations
Department Goal 1: Students should
This will be demonstrated on homework and
develop skills in problem-solving.
on exams.
Department Goal 2:
Class discussions will require informal oral
Students should develop their ability to
communication. Homework and exams will
communicate mathematical ideas.
require more formal written communication.
Department Goal 4:
The course includes an introduction to
Students should be aware of a broad
optimization in applied settings. This will be
variety of applications, both in and out of demonstrated on homework and on exams.
mathematics.
Department Goal 5:
This course builds on students’ backgrounds
Students should recognize the breadth of in linear algebra and discrete mathematics,
mathematics and experience the
and thus provides depth in a mathematical
intellectual rigor of depth in an advanced subject. This will be demonstrated on
subject area.
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 have a better understanding
of the material than those who miss classes.
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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 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 Tuesday October 8.
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 Tuesday November 12.
 The paper will examine an application of Operations Research. This is discussed
in more detail below.
 The Final Exam will be TUESDAY DECEMBER 10 at 3:00-6:00. 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 as follows:
A+
A
AB+
B
BC+
C
CD+
D
DF
Impress me!
92% or higher
88 – 91%
84 – 87%
79 – 83%
75 – 78%
70 – 74%
63 – 69%
60 – 62%
58 – 59%
52 – 57%
50 – 51%
0 – 49%

Homework: 8 assignments
at 25 points each
200 points
Test 1
150 points
Test 2
150 points
Paper
100 points
Final Exam
250 points




Your course grade will be your point total as a percentage of the 850 possible points.
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I. UNIVERSITY POLICIES
Attendance 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.
Academic Honesty
I strongly endorse and will follow the academic honesty policy as published in the Bellarmine
University Course Catalog, available on the university website. Students and faculty 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.
Definitions of each of these forms of academic dishonesty are provided in the academic honesty
section of the Course Catalog.
All confirmed incidents of academic dishonesty will be reported to the Assistant Vice President
for Academic Affairs for Academic Operations, and sanctions will be imposed as dictated by the
policy. The instructor’s choice of penalty ranges from a minimum penalty of failing the
assignment or test to failing the course itself, and if the student has a record of one prior offense,
he or she will be suspended. This sanction is in addition to the penalty imposed by the faculty
member. If the student has a record of two prior offenses, he or she will be immediately and
permanently dismissed from the university upon the third offense. It is generally assumed that
graduate students fully understand what accounts for academic dishonesty. Thus, no
leniency of penalty will be applied in cases involving graduate students.
Academic Resource Center (ARC)
Bellarmine University is committed to providing services and programs that assist students in
further developing their learning and study skills and in reaching their academic goals. Students
needing or wanting additional and/or specialized assistance should seek out the resources of the
ARC, located on the A-level of the W.L. Lyons Brown Library. Call 272-8071 for more
information
Disability Services Statement:
Students with disabilities who require accommodations (academic adjustments and/or auxiliary
aids or services) for this course must contact the Disability Services Coordinator, located in the
Counseling Center (Allen Hall), phone 272-8480. Students are encouraged to make these
arrangements with the Disability Services Coordinator as early in the semester as possible so that
a student and his/her course instructor can collaborate for a successful course experience.
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J. 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 list on the website. 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 how they were applied to the particular
situation. I am particularly interested in the underlying mathematics used in the application.
Some specific requirements:

Your selection, including a copy of the article, must be turned in no later than Thursday,
Oct. 10. 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 Tuesday, November 19 at the beginning of class; later that day is
LATE! I will deduct 10 points for each day the paper is late.
Your paper will be graded by the rubric on the next page.
5
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 method is correctly identified.
The application of the algorithm is clearly explained.
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.
The paper lacks some organization.
Some main points are not clear.
The paper has a conclusion.
The method is correctly identified.
The explanation of the algorithm 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 method is not correctly identified.
There are significant errors in explaining the algorithm.
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.
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MATH 430 Operations Research
Ch. 1: Introduction
Ch. 3:
Basic Ideas
of LP
Ch. 2: OR Modeling
Ch. 4:
The Simplex Method
Ch. 5: Theory
Ch. 11:
Integer LP
Ch. 6:
Duality &
Sensitivity
Ch. 8: Special
Forms of LP
Ch. 9: Networks
Ch. 14:
Game Theory
Ch. 22: CPM and PERT
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HOMEWORK ASSIGNMENTS
Assignment Chapter Tentative due date
Pages
Problems
#1
3
Tuesday Sept. 10
77-82
3.1 – 2, 5, 9, 11, 12
3.2 - 2, 3, 4, 5
3.3 - 1, 2
3.4 – 3, 5, 9, 12
#2
4
Tuesday Sept. 24
150-157 4.1 - 1, 4, 8
4.2 – 1ab
4.3 – 2, 8
4.4 - 1, 7
4.5 - 1, 4, 8
4.6 - 1, 3, 8ac, 11, 13, 14, 17
4.7 – 5
#3
5
Tuesday Oct. 1
188-193 5.1 – 3, 4, 10, 14, 16, 17a, 18, 20, 21
5.3 - 1, 2, 5
Test 1
Tuesday Oct. 8
#4
6
Tuesday Oct. 22
261-268 6.1 - 1, 2, 3, 8, 11
6.3 - 1, 5
6.4 – 1, 3, 4
6.5 – 1
6.6 – 2
6.7 – 2abcdef, 8
#5
8
Tuesday Oct. 29
348-354 8.1 - 2, 3, 4
8.2 – 1c, 5, 6, 8, 11, 21abcd
8.3 – 1ab, 2, 4
8.4 - 1, 4, 6
#6
11
Tuesday Nov. 5
524-531 11.1 – 2ac, 4, 5
11.3 – 1, 4, 5, 7
11.4 – 1, 5
11.5 – 2, 6
11.6 - 1, 2, 6
11.7 – 2ab, 6, 9, 10
Test 2
Tuesday Nov. 12
#7
9
Thursday Nov. 21
412-415 9.2 – 1
9.3 – 3ab, 4, 7
9.4 - 1, 2, 3
22
22:42-47 22.2 – 1, 2
22.3 – 2, 3
22.4 – 1, 2abd
#8
14
Tuesday Dec. 3
668-671 14.1 - 1, 3
14.2 - 1, 2, 3, 4, 5, 6
14.4 – 3, 4
14.5 – 2, 3
Final Exam
Tuesday Dec. 10
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