OR642: Combinatorial and Integer Programming


Systems Engineering and Operations Research Department

Time:              Mondays, 4:30-7:10p.m; David King Hall 2053

Professor Karla L. Hoffman
Office:            SciTech Building II, Room 119
Phone:            (703)993-1679 or 993-1670 (secy); 993-1521 (fax)
email:             khoffman@gmu.edu
url:                  iris.gmu.edu/~khoffman

Homepage for course:  http://iris.gmu.edu/~khoffman/or642_s04/or642_s04.html

Office hours: Mondays: 2:00-3:30p.m. and by appointment

Text:               Wolsey, L. Integer Programming  Wiley, Interscience, 1998.

Software:        You will be expected to use a modeling language to complete your project. You will be required to use the MPL modeling language (unless other arrangements are made with Dr. Hoffman).  Mr. Stephen Charbonneau will be presenting some background lectures on how to use advanced indexing and how to embed VBA into your modeling effort.

        MPL (Maximal Software) available by downloading from the internet lab and they will download for you. (www.maximal-usa.com)

Course Description: This course is designed to introduce discrete optimization models and to provide the mathematical foundations of integer and combinatorial optimization models along with the algorithms that can be used to solve such problems. The course will stress the explosion of new results in integer and combinatorial optimization The problem areas discussed will include planning models such as capital budgeting, facility location and portfolio selection, and design problems such as telecommunication and transportation network design, VLSI circuit design and the design of automated production systems. Examples from statistics, economcis, politics and mathematics will also be presented. Polyhedral theory necessary to understand the new techniques will be covered in some detail. A tentative outline of the topics is provided below. This outline can change based on time limitations and the interests of the students. Although the text required will be used as much as possible, there will be much supplemental material covered.

Course Outline

Topic I.     Introduction to discrete optimization. 

             Formulations and modeling.

Topic II.    Linear programming review with emphasis on the dual. 

Topic III.   Optimality, Relaxation, and Bounds 

Topic IV.    Approaches to solving integer programming problems 

       Total enumeration, 
       Implicit enumeration,
       Bounding algorithms 
       Tree search

Topic V.     Relaxation and decomposition techniques 

       Lagrangian relaxations 
       Linear-programming relaxations 

Topic VI.   Heuristic Procedures 

       Performance measures for classic algorithms
       Lp-based algorithms
       New techniques (e.g. Tabu Search, Genetic algorithms, simulated annealing) 

Topic VII.   Cutting plane approaches

       Branch and Cut 
       Polyhedral Theory
       Facet Identification for structured integer programs

Topic VIII.  Column generation procedures

Homework problems will be assigned at each session.  Some or all of the assignments will be collected and graded. 



It is likely that the mid-term will be in-class and the final will be a take-home exam.  In class exams will be open book and open notes. There will also be one project that will require the formulation and solution of a collection of integer programming problems.  The project can be done jointly with one other student, or individually.


The midterm will count for 25% of the grade, the take-home final will count for 35% of the grade, homework assignments will be averaged and count for 20% of the grade and the project will count for 20%,



 Fundamental Rules:



(1) Make-up exams will only be given for extreme situations, and only if I am contacted before the exam is given and full arrangements are established.  Full adherence to this policy is the responsibility of the student.


(2) The exam dates above are tentative, and it is the student's responsibility to keep abreast of changes.


(3) Homework will be assigned each class, and usually collected.  All work must be clearly written.  Illegible work will not be accepted.


(4) There is a penalty of 10% of the total grade for every day homework is late.