General+Information


 * __ Course Description __**

Optimization problems arise in a wide variety of systems including manufacturing systems, transportation systems, financial systems, and telecommunication systems. This course covers major mathematical models of optimization problems -- linear programming, network flow, integer programming, and nonlinear programming. We will focus on formulation issues and solution methodologies for these classes of optimization models.

Excerpt from the first article quoted about G.B. Dantzig: "Dr. Dantzig's seminal work allows the airline industry, for example, to schedule crews and make fleet assignments. It's the tool that shipping companies use to determine how many planes they need and where their delivery trucks should be deployed. The oil industry long has used linear programming in refinery planning, as it determines how much of its raw product should become different grades of gasoline and how much should be used for petroleum-based byproducts. It's used in manufacturing, revenue management, telecommunications, advertising, architecture, circuit design and countless other areas."

We will use several optimization software packages, first the easy-to-use commercial packages, LINDO and possibly EXCEL. These are good for small problems but data entry can be tedious. Another class of solvers work on algebraic formulations, and are useful in particular when one must solve several problems with the same structure, such as transportation or assignment problems. One of these is LINGO, an extension of LINDO, also available on the CD that comes with the text. Another one is GAMS (General Algebraic Modeling System). It is both an interface between us, the users, and commercial "solvers", i.e., software packages that are designed to solve one or more of the model types mentioned above, and a language, in which one can write models and to some extent algorithms for solving them, using, or not, the solvers provided. GAMS is available on a number of servers on campus.

__** Who is this course for? **__

This course is intended as a first course in Mathematical Programming for graduate students in engineering, mathematics, statistics, marketing and operations management/research. This section is specially designed for doctoral students, who will most likely take some more advanced courses after this one, such as Advanced Linear Programming, Advanced Nonlinear Programming, Advanced Integer Programming, Graph Theory, and so on. More emphasis will be placed on algorithms, the underlying theory, and on matrix representations.

__** Background **__

This course assumes elementary background in multivariate differential calculus and in linear algebra, plus familiarity with vector/matrix notation and arithmetic.

__ Grading Policy __

 * Projects: 25%
 * Homework: 25%
 * Midterm Exam: 25%
 * Final Exam: 25%