# Fall 2022 - MATH 308 D400

## Overview

• #### Course Times + Location:

Sep 7 – Dec 6, 2022: Mon, 2:30–4:20 p.m.
Surrey

Sep 7 – Dec 6, 2022: Wed, 2:30–3:20 p.m.
Surrey

• #### Exam Times + Location:

Dec 15, 2022
Thu, 3:30–6:30 p.m.
Surrey

• #### Instructor:

Abraham Punnen
apunnen@sfu.ca
1 778 782-7611
• #### Prerequisites:

MATH 150, 151, 154, or 157 and MATH 240 or 232, all with a minimum grade of C-.

## Description

#### CALENDAR DESCRIPTION:

Linear programming modelling. The simplex method and its variants. Duality theory. Post-optimality analysis. Applications and software. Additional topics may include: game theory, network simplex algorithm, and convex sets. Quantitative.

#### COURSE DETAILS:

Linear Programming

Formulation of optimization problems as linear programs and solutions using the Microsoft Excel solver, Open solver and GUROBI
Two variable linear programs
Convex polytope and extreme points
The Fundamental Theorem of linear programming.

The Simplex Algorithm

Simplex Tableaus
Revised simplex algorithm
Degeneracy and cycling

Duality Theory

Dual of a linear program and interpretations
The dual simplex algorithm
Complementary slackness
The strong duality theorem.

Post optimality and Parametric Analysis

Post-optimality analysis (Adding and deleting variables, adding and deleting constraints (cutting planes))
Sensitivity Analysis

Network Models

Minimum cost flows
Transportation problem
Assignment problem.
Other Applications (as time permits)

Assignments

Assignments will be posted on the course web page on each Wednesday.  Solutions are due the following Wednesday 4:30 pm in the assignments drop box.

There will be no make-up midterm tests. The weight for a missed test (for medical reasons) will be added to the weight for the final examination. Missed assignments will earn zero credit. There will be a total of 10 assignments of which the best 8 will be considered for final grade calculations.

• Midterm 1 15%
• Midterm 2 15%
• Assignments/ Quizzes 20%
• Final Exam 50%

#### NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semesters.

#### REQUIREMENTS:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient).

## Materials

#### MATERIALS + SUPPLIES:

Some Maple worksheets will be posted on Canvas.

Linear Programming and Network Flows
Bazaraa, Mokhtar S ; Jarvis, John J ; Sherali, Hanif D
4th Edition, Wiley

ISBN: 9780470462720

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

#### Registrar Notes:

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html