Linear Programming
A'04 Course Information

MA 3231 Section A01 Mon, Tue, Thu & Fri: 8 am. SH203

Instructor:

Office: SH104C
Phone: x 5495
Classes & Office Hours:

Monday Tuesday Wednesday Thursday Friday
Lectures
@ SH203
8:00-8:50 am 8:00-8:50 am - 8:00-8:50 am 8:00-8:50 am
Office Hours
@ SH104C
*)
- 2:00-2:50 pm - - 1:00-1:50 pm
____________
*) Also available by appointment

Course Objectives:

The course's primary aim is to introduce the students to a wide range of real-world optimization problems and their interpretation as linear programs and discuss the aspects of the Simplex Method - the basic instrument of their solution.

Upon completing the course the students will:

learn the terminology of Linear Programming,
understand how the Simple Method works, and
find out how to formulate and solve the relevant real-life problems.

Main Topics: Course Contents:
• Introduction to Linear Programming
• The Simplex Method (including the
Big-M and the two-phase methods)
• Sensitivity Analysis & Duality
• Related MATLAB computation

Four 1-hour lectures a week
Homework problems - Quizzes
Two MATLAB projects
Midterm
Final Exam
Useful Resources:

Main Text:

M.S. Bazaraa, J.J. Jarvis, and H.D. Sherali, Linear Programming and Network Flows, 2nd Edition, John Wiley, 1990.

Other Sources:
Course Web Page:

The 100% course grade is based on:

Topic Quizzes (25%, 5 times, 5% each),
Projects (30%, 2 projects, 15% each),
Midterms (20%),
Final Exam (25%).

Point ranges derived to percents for grades are given by:

Percentage 90.00 80.00 - 89.99 70.00 - 79.99 69.99

Homework & Quizzes:

Many valuable aspects of the course material will be supported by practical exercises to be made at home. The list of recommended problems can be found on the Homework Assignments page.

Papers with the homework problems will not be handed in, so each student should take a personal responsibility for doing sufficient study and practice.

There will be five 15-min quizzes composed from the selected homework problems assigned in the preceding classes. Using notebooks will be allowed when doing the quiz.

MATLAB Projects:

Your work on the 2nd and 3rd main topics will be accompanied by two projects. They should be completed by the end of corresponding parts of the course and presented to the class in the MATLAB Project Days. The printed reports are due in class the same days (see Schedule of Events below.)

The objective of the projects is essential for the course: they should give you an experience in using the LP methods for solving applied real-life problems. You will work on the projects in pairs; the pairs should be formed by Mon, August 30 (partially by assignment).

To complete the projects, additional reading and MATLAB practicing may be necessary. The project tasks and instructions can be found on the MATLAB Projects page.

Midterm & Final Exam:

There will a Midterm covering Part 1 of the course; in the Final Exam you will demonstrate your familiarity with the material of Parts 2 and 3.

The Midterm and the Final are open-book & open-notes events. Two days prior to the test, its description will appear on the Test Preview page. Partial take-home policy will be applied: the theoretical problems will be posted there, so you could think of them in advance (and even collaborate with your classmates). No notes, however, will be allowed when answering those questions during the tests.
Bonuses & Other Policies:

There will be opportunities to earn bonus points. The Midterm and the Final will contain bonus problems. Also, the outstanding projects can be awarded by some bonuses at the instructor's discretion.

Students are responsible for learning the basics of MATLAB on their own. Supportive material (including the links to the Internet resources) is provided on the web page about the related MATLAB Scripts. It is therefore presumed that the class discussion of the MATLAB technicalities will be reduced to a minimum.

No make up of the missed Quizzes and the Midterm will be possible, and no late Project submissions will be accepted unless there is a legitimate reason which can be documented (an illness or another unavoidable emergency).

All important course-related information which becomes available (including answers to FAQ) will be posted on the Announcements & Hints page.

Part I: Introduction to Linear Programming: August 26 - September 10
Part II: The Simplex Method: September 13 - September 28
Part III: Sensitivity Analysis and Duality: September 30 - October 12

Week 1: Structure, stages and formulations of an LP problem. Related topics in linear algebra and geometry.
• Lecture meetings: August 26, 27, 30, 31
Week 2: Graphical solution of two-variable LP problems. Unique optimal solution and other cases: alternative or multiple optimal solutions, infeasible LP problems, unbounded LP problems.
• Lecture meetings: September 2, 3, 7
• Quiz # 1: Fri, September 3
Week 3: LP problem's standard form. Preview of the Simplex algorithm: basic and nonbasic variables, feasible solutions, direction of unboundedness.
• Lecture meetings: September 9 (Midterm preview), 13, 14
• Midterm: Fri, Sept 10
Week 4: Optimal basic feasible solution. The Simplex algorithm in more details. Simplex tableau. Formulations for max and min problems. Unbounded LP problems.
• Lecture meetings: September 16, 17, 20, 21
• Quiz # 2: Thu, September 16
Week 5: Degeneracy and the convergence. The Big-M method and the two-phase method. Sensitivity analysis: graphical introduction.
• Lecture meetings: September 24, 27, 28
• MATLAB Project Day (reports are due): Thur, September 23
• Quiz # 3: Fri, September 24
Week 6: Sensitivity analysis: analytical approach. The dual of an LP problem and the dual theorem. Duality and sensitivity.
• Lecture meetings: September 30, October 1, 4, 5
• Quiz # 4: Fri, October 1
Week 7: The dual simplex method.
• Lecture meeting: October 7, 11 (Exam preview)
• MATLAB Project Day (reports are due): Fri, October 8
• Quiz # 5: Thu, October 7
• Final Exam: Tue, October 12, 8-9 am (SH203)

Course Information | Homework Assignments | MATLAB Projects | Test Preview | Announcements & Hints

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