Fall 2024 - MATH 708 G100

Discrete Optimization (3)

Class Number: 3864

Delivery Method: In Person


  • Course Times + Location:

    Sep 4 – Dec 3, 2024: Mon, 2:30–4:20 p.m.

    Sep 4 – Dec 3, 2024: Wed, 2:30–3:20 p.m.



Held jointly with MATH 408-3. See description for MATH 408-3. Students may not take a 700-division course if it is being offered in conjunction with a 400-division course which they have taken previously.


Model building using integer, binary and mixed integer variables.  Computer solution of integer programming models, linear programming relaxations, duality, simple upper bounds using greedy algorithms.  Branch and bound algorithms, implicit enumeration, LP based branch and bound.

Valid inequalities, Gomory's fractional cut, mixed integer cuts, strong valid inequalities, simple facets for the 0-1 knapsack polytope and the traveling salesman polytope, branch and cut algorithms.

Lagrangian relaxation, strength of the Lagrangian dual, Lagrangian heuristics.

Column generation algorithm, solving the symmetric traveling salesman problem using column generation.

Greedy and local search algorithms, construction heuristics, worst case analysis of heuristics.


  • Individual Homework 40%
  • Team Homework 15%
  • Project 15%
  • Midterm Exam 10%
  • Final Exam 20%


MATH 708 is cross-listed with MATH 408. Students registered for Math 708 will be required to design and deliver a presentation to the Math 408/708 on an advanced topic chosen in consultation with the instructor.  The will also have to complete additional questions on the assignments and tests.



Integer Programming
Zambelli, G. Conforti, M. and Cornuejols, G.
Springer, 2016

Online access to this text via the SFU library: 


The 2014 and the 2016 versions are the same except for the ISBN.
ISBN: 9783319384320


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Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

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


Students with a faith background who may need accommodations during the term 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.