Fall 2023 - MATH 308 D400
Linear Optimization (3)
Class Number: 2078
Delivery Method: In Person
Course Times + Location:
Sep 6 – Dec 5, 2023: Mon, 2:30–4:20 p.m.
Oct 10, 2023: Tue, 2:30–4:20 p.m.
Sep 6 – Dec 5, 2023: Wed, 2:30–3:20 p.m.
Exam Times + Location:
Dec 8, 2023
Fri, 8:30–11:30 a.m.
1 778 782-7611
Prerequisites:MATH 150, 151, 154, or 157 and MATH 240 or 232, all with a minimum grade of C-.
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.
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
- 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
- Minimum cost flows
- Transportation problem
- Assignment problem.
- Other Applications (as time permits)
There will be 10 assignments of which best seven will be counted towards the final grade.
There will be three midterm tests. No make-up midterm tests are provided. Students missing one or more midterm tests (with approval of instructor) can write a comprehensive final examination to be scheduled along with all other make-up final examinations, generally on the first day of Spring Term, 2024. The weight of this final examination will be equal to that of the missing midterm test(s).
- Assignments 15%
- Final Project 15%
- Midterm Test 1 20%
- Midterm Test 2 25%
- Midterm Test 3 25%
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.
No required textbook. Lecture notes will be provided.
REQUIRED READING NOTES:
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.
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Students with a faith background who may need accommodations during the semester are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.