Spring 2007 Home Page

Welcome to the Math 428, Principles of Operations Research, home page. You're probably here for information, so let's start with the vital statistics of the course.

Essential Information

Operation Research Resources

As we all know, lots of information can be found on the web. Go to your favorite search engine (like the Yahoo site listed on my home page) and try searching on "operations research resource". See how many web pages you hit and visit a few interesting looking sites. As we cover specialized topics, try searching on them with keywords such as "simplex method".


Notes and FAQ

1/9/06:(Just to get the FAQ started) About significant digits...
I've been asked to explain what "significant digits of an approximation" to a (nonzero) number means. There are several interpretations that one commonly sees. The "absolute" definition, which is perhaps more intuitive, goes as follows: to get the number of significant digits, first *subtract* (rather than just looking at the numbers) the two (may as well be larger - smaller), then find the position of the leading digit of the error relative to the position of leading digit of the exact answer. (We're thinking in fixed point representation in this discussion). If the difference in that position is less than 5, then number of significant digits is one less than the difference, else two less.

For example if 3.14 and 3.15 are used to approximate 3.14159, calculate 3.14159 - 3.14 = 0.00159 and 3.15 - 3.14159 = 0.00841. Notice I put a zero in front of the decimal to start counting from the right position. There is a nonzero digit at the 4th position with each approximation, counting from the (base 10) position of the leading digit of 3.14159. The size of this digit is at most 5 in the first case, so this approximation has 3 significant digits. In the second case, the digit is larger than 5, so the approximation only has 2 significant digits.

The "relative" definition is usually preferred in numerical analysis and it goes as follows: if xapprox is used to approximate xtrue, the number of significant digits is largest integer n such that the relative error, |(xapprox-xtrue)/xtrue)| is no larger than 5x10^(-n-1). In our previous example the relevant quotients are 0.000506 and 0.002677, respectively. Thus, this definition will give only 2 significant digits in both cases. In general, the "relative" definition is stingier than the "absolute" one. Hope this helps.

Class Policy Statement

Course: Math 428, Introduction to Operations Research

Place/Time: 12 AvH, 2:00-3:45 TR, Spring 2007

Preq: Math 314 and Stat 380 or equivalent.

Objectives: To help students achieve competence in the following areas:

  • Basic principles of operations research techniques including linear programming, decision analysis and queueing theory.
  • Understanding of how to apply these techniques to real world problems.
  • Use of numerical and computer tools for solving these problems.
Instructor: Dr. Thomas Shores

Telephone: Office 472-7233   Home 489-0560

Email: tshores1@math.unl.edu

Web Home Page: http://www.math.unl.edu/~tshores1/

Office Hours: Monday 2:00-3:30, Tuesday 11:00-12:30, Thursday 3:30-5:00, Friday 8:30-10:30, and by appointment. Office: 229 AvH

Class Attendance: Is required. If absent, it is incumbent upon the student to determine what has been missed as soon as possible. It is advisable to consult with the instructor.

Homework/Projects: Homework will be assigned in class and collected in accordance with the syllabus, and will be usually returned within one week. Although collaboration in solving most problems is encouraged, it is strictly forbidden to copy someone else's homework. It is expected that co-collaborators and other sources for the homework will be duly acknowledged. For some specified problems no collaboration will be allowed. There is no official programming language for this course and prior programming experience is not required. Current information about the course will be available through Blackboard and the 428 homepage. Using the web is strongly recommended for keeping track of current activities in the course.

Reading Assignment: Read the sections of the texts as, or before, they are covered in class lectures. This is a standing assignment throughout the semester.

Grade: One midterm will be given and will account for 135 points. The final exam will count 140 points. Each exam may have a take home component. In-class exams are closed book with calculators. Homework will count 225 points. The final grade will be based on these 500 points.

Final Exam: Will be comprehensive. To be given on Monday, April 30, 1:00 - 3:00 pm in 12 AvH.

Grades of "I", "W" or "P": These grades will be given in strict accordance with University policy. (See any Schedule of Classes for the relevant information and dates.)

Keep This Information!!!

Syllabus for Math 428, Spring 2007

  • TEXT: Introduction to Operations Research, Eighth Edition, Frederick Hillier and Gerald Lieberman, McGraw-Hill, New York, 2005.
  • ISBN: 0-07-252744-7

The times listed below are approximate, and may be adjusted as the semester progresses. The two sources for material are the class textbook (BT) and my own prepared notes (NT). Assignments are due on Tuesday if they are listed first below, and Thursday otherwise. Unless otherwise stated, you should turn in hardcopy of your work. The specifics of each assignment will be given in class and posted on the web as the course progresses. Problems that are to be worked by individuals without collaboration will be marked ``(I)''. Each assignment will be worth 45 points. Each assignment includes all problems not yet collected and assigned one week or more before the due date.


1 Jan 8-12 1.1-4 Introduction
    2.1-6 Overview of OR
    3.1 Prototype LP example

2 Jan 15 (no class) Martin Luther King Day
  Jan 16-19 3.2-4 LP model and examples

Friday, January 19, is the last day to withdraw from the course and not have it appear on your transcript.

3 Jan 22-26 3.5-8 Examples and programming

4 Jan 29-Feb 2   Asgn 1 due
    4.1-5 Principles of simplex method

5 Feb 5-9 4.6-10 Analysis of simplex method

6 Feb 12-16 5.3, 6.1-5 Duality and sensitivity
      Asgn 2 due

7 Feb 19-23 6.6-9 Applying sensitivity analysis

8 Feb 26-Mar 2   Midterm
    15.1-4 Decision prototypes and basics

Friday, March 2, is the last day to change your grade option to or from ``Pass/No Pass''.

9 March 5-9 15.5-8 Applications and utility theory
      Asgn 3 due

10 Mar 12-16 (no class) Spring Break

11 Mar 19-23 17.1-5 Queueing theory basics and models

12 Mar 26-30 17.6-11 Applications and calculations

13 Apr 2-6 18.1-4 Inventory models and examples
      Asgn 4 due

Friday, April 6, is the last day to withdraw from the course and receive a grade of W.

14 Apr 9-13 18.5-9 Stochastic models and calculations

15 Apr 16-20 20.1-5 Simulation and random numbers

16 Apr 23-27 20.6-8 Simulation calculations
      Asgn 5 due

Final Exam: The final exam is a comprehensive exam to be given on Monday, April 30, 1:00 - 3:00 pm in 12 AvH.

Department Grading Appeals Policy: The Department of Mathematics does not tolerate discrimination or harassment on the basis of race, gender, religion or sexual orientation. If you believe you have been subject to such discrimination or harassment please contact the department. If, for this or any other reason, you believe that your grade was assigned incorrectly or capriciously, appeals may be made to (in order) the instructor, the department chair, the departmental grading appeals committee, the college grading appeals committee and the university grading appeals committee.