Important Information
The
syllabus contains most of the key information for the course.
Resources
The course
textbook. (Updated April)
Additional notes on
Integer Programming Methods.
We will be exploring many
modeling problems during February in class. Please read one or two problems ahead of what we have completed in class.
Please consider this
example of how to write acceptable homework solutions. Here is a more detailed
example.
Refresher on
partial derivatives.
Another refresher on
partial derivatives.
Addtional practice on finding
extrema of functions.
How to find
eigenvalues of a matrix.
How to find the
determinant of a matrix.
George Dantzig wrote a nice
article on the early days of the Simplex Method for solving linear programs.
Some problems ask you to compose summary documents such as this example
Executive Summary. I believe that it is a very valuable skill to be able to concisely and accurately summarize your work.
Homework
(##) [Due Date] Assignment, due in class unless otherwise specified
(01) [Mon Jan 14] (by 4 PM) Section 2, Exercises 1,2,3,4.
(02) [Tue Jan 22] Section 3, Exercises 3,4,5c,5d,6,8c,8d AND Section 4, Exercises 1,2.
(03) [Tue Jan 29] Section 4, Exercises 4,6d,6f AND Section 5, Exercises 2,3,6,7.
(04) [Tue Feb 05] Section 6, Exercises 2,3 AND Section 7, Exercises 1,2. For some of these exercises, you will need access to Matlab or Octave software. There are many options: (1) personal copy, (2) Math department software, (3) octave-online.net .
(05) [Tue Feb 12] Section 8, Exercises 3-8 AND Section 9, Exercises 1,5.
(06) [Tue Feb 19] Section 11, Exercises 2-5 AND Modeling Problems 4,8.
(07) [Tue Feb 26] Section 11, Exercises 6,8 AND Modeling Problems 5,7.
(08) [Tue Mar 05] Section 11, Exercises 9,10,11 AND Modeling Problem 20.
(09) [Tue Mar 19] Section 11, Exercise 12 AND Modeling Problem 10.
(10) [Tue Mar 26] Section 11, Exercises 15,17 AND Modeling Problems 16,19.
(11) [Tue Apr 02] Section 12, Exercises 1,2,3 AND Section 13, 3,6,7a.
(12) [Tue Apr 09] Section 13, Exercises 7b,c,d,e,f and 10,11.
(13) [Tue Apr 16] Consider the Puzzles and Games Inc. Problem of Section 11.17 and the formulation which does NOT enforce the "either-or" manufacturing constraint. Show that the optimal solution of the LP Relaxation is not integer-valued. Carefully solve the integer program using either the Branch and Bound method or the Cutting Plane method. You may use software to solve any LP Relaxation problems that arise in your solution process.
(14) [Tue Apr 23] Section 11, Modeling Problem 17. Model the problem as a binary integer program, then solve using the method of Implicit Enumeration.
Quiz Solutions
Week 3.
Week 4.
Week 5.
Week 7.
Week 8.
Week 9.
Week 11.
Week 12.
Week 13.
Your quiz for week 15 is to complete the online course evaluation. This is
a bonus quiz in that I will drop one extra low quiz score for everyone who
completes this task.
Midterm Exam
Date: Thursday March 7, 2019
Time: 9:10-10:25 (normal class time)
Location: Our normal classroom
Here is the exam cover sheet and the writing assignment problem.
You may wish to look over this
example midterm from last semester. Our midterm
will cover similar material, but may not be of this particular format. The
level of skills and knowledge demonstration are representative of what I will
expect of you.
Final Exam
Date: Friday May 3, 2019
Time: 10:10-12:10
Location: Our normal classroom
The exam will test your content knowledge and application skills in the areas
of optimization which we considered throughout the course. The exam will
consist of seven parts (questions) on the following topics.
- Constrained and unconstrained optimization of smooth functions using calculus methods.
- Standard forms of linear programs.
- Modeling mixed-integer programs whose solutions answer optimization questions from finance, mathematics, business or planning.
- Composing executive summaries or business memos which summarize optimization findings for the intended audience.
- Concepts and practice of the Simplex Method.
- Concepts and practice of solving integer programs.
- Concepts and practice of interior point methods in optimization.
