# Spring 2023 - MATH 308 D100

## Overview

• #### Course Times + Location:

Mo, We, Fr 2:30 PM – 3:20 PM
WMC 3260, Burnaby

• #### Exam Times + Location:

Apr 20, 2023
3:30 PM – 6:30 PM
WMC 3520, Burnaby

• #### Instructor:

lstacho@sfu.ca
1 778 782-4816
• #### 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

Linear optimization is a mathematical method for computing a best solution (such as maximum profit or minimum cost) in a given mathematical model for some set of requirements satisfying a linear relationship. It can be applied to various problems of business, economics, engineering and other industries where diverse types of problems in planning, routing, scheduling, assignment, and design have to be modelled and solved.

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

There will be six assignments due bi-weekly. Every other week, there will be an in-class quiz (six quizzes in total). The due date will be determined at the beginning of the term. Only the best nine assignments and quizzes, respectively, will be considered for the final grade calculations.

There will be one midterm exam. There will be no make-up midterm test. The weight for a missed test (for medical reasons) will be added to the weight for the final examination.

• Assignments 15%
• Quizzes 15%
• Midterm 30%
• Final Exam 40%

#### 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.

No required textbook. Lecture notes will be provided.

Linear Programming and its Applications by James K. Strayer, Springer-Verlag, NY, 1989.

ISBN: 0-387-96930-6